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Stats 7.2

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What kind of sampling method would this be?

Convenience sampling

A critical value, zα, denotes the _______.

Hw 7.2 (17) z dash score with an area of alpha to its right.

is useful for determining whether the claimed rate is incorrect.

Part (b)

Which of the following is NOT a property of the chi-square distribution?

The mean of the chi-square distribution is 0.

Do one of the following, as appropriate. (a) Find the critical value zα/2, (b) find the critical value tα/2, (c) state that neither the normal nor the t distribution applies. Confidence level 99%; n=20; σ is known; population appears to be very skewed.

neither normal nor t distribution applies

Which of the following is NOT an equivalent expression for the confidence interval given by 161.7<μ<189.5?

161.7±27.8

The percentage of women who are too tall to fit through a standard door without bending is 00

The sample means target the population mean. In general, sample means do make good estimates of population means because the mean is an unbiased estimator.

1. target 2. do 3. unbiased

Given these results, does it seem that the candy company is providing consumers with the amount claimed on the label? Yes, because the probability of getting a sample mean of 0.8536 g or greater when 449 candies are selected is not exceptionally small.

1. yes 2. is not

Which of the following is NOT an observation about critical values?

A critical value is the area in the right-tail region of the standard normal curve.

A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 45.0 and 55.0 minutes. Find the probability that a given class period runs between 51.25 and 51.75 minutes.

HW 6.2 (3)

Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard deviation 1.

HW 6.2 (4)

Do the new ratings appear to be safe when the boat is loaded with 14 passengers? Choose the correct answer below.

Because there is a high probability of overloading, the new ratings do not appear to be safe when the boat is loaded with 14 passengers.

The _____________ distribution is used to develop confidence interval estimates of variances or standard deviations.

Chi-square

The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 0 and 9 minutes. Find the probability that a randomly selected passenger has a waiting time greater than 1.25 minutes.

HW 6.2 (2)

Find the area of the shaded region. The graph depicts the standard normal distribution of bone density scores with mean 0 and standard deviation 1.

HW 6.2 (5)

Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1.

HW 6.2 (6)

Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1.

HW 6.2 (7)

Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1.

HW 6.2 (8)

Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. Find the probability that a given score is less than 1.71 and draw a sketch of the region.

HW 6.2 (9)

Use the data in the table to the right to answer the following questions. Find the sample proportion of candy that are red. The proportion of red candy=nothing (Type an integer or decimal rounded to three decimal places as needed.)

HW 7.2 (10)

During a period of 11 years 1594 of the people selected for grand jury duty were sampled, and 33% of them were immigrants. Use the sample data to construct a 99% confidence interval estimate of the proportion of grand jury members who were immigrants. Given that among the people eligible for jury duty, 37.8% of them were immigrants, does it appear that the jury selection process was somehow biased against immigrants?

HW 7.2 (11)

Use the given data to find the minimum sample size required to estimate a population proportion or percentage. Margin of error: 0.04; confidence level 95%; p and q unknown

HW 7.2 (12)

Many states are carefully considering steps that would help them collect sales taxes on items purchased through the Internet. How many randomly selected sales transactions must be surveyed to determine the percentage that transpired over the Internet? Assume that we want to be 95% confident that the sample percentage is within five percentage points of the true population percentage for all sales transactions.

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Find the sample size, n, needed to estimate the percentage of adults who have consulted fortune tellers. Use a 0.03 margin of error, use a confidence level of 95%, and use results from a prior poll suggesting that 13% of adults have consulted fortune tellers.

HW 7.2 (14)

A programmer plans to develop a new software system. In planning for the operating system that he will use, he needs to estimate the percentage of computers that use a new operating system. How many computers must be surveyed in order to be 90% confident that his estimate is in error by no more than four percentage points? Complete parts (a) through (c) below.

HW 7.2 (15)

The brand manager for a brand of toothpaste must plan a campaign designed to increase brand recognition. He wants to first determine the percentage of adults who have heard of the brand. How many adults must he survey in order to be 95% confident that his estimate is within eight percentage points of the true population percentage? Complete parts (a) through (c) below.

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Find the critical value zα/2 that corresponds to the given confidence level. 93%

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Express the confidence interval 0.222<p<0.888 in the form p±E.

HW 7.2 (4)

Express the confidence interval (0.079,0.125) in the form of p−E<p<p+E.

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Use the sample data and confidence level given below to complete parts (a) through (d). A research institute poll asked respondents if they acted to annoy a bad driver. In the poll, n=2366, and x=911 who said that they honked. Use a 90% confidence level. LOADING... Click the icon to view a table of z scores.

HW 7.2 (7)

In the week before and the week after a holiday, there were 10,000 total deaths, and 4934 of them occurred in the week before the holiday. a. Construct a 95% confidence interval estimate of the proportion of deaths in the week before the holiday to the total deaths in the week before and the week after the holiday. b. Based on the result, does there appear to be any indication that people can temporarily postpone their death to survive the holiday?

HW 7.2 (8)

An online site presented this question, "Would the recent norovirus outbreak deter you from taking a cruise?" Among the 34,857 people who responded, 64% answered "yes." Use the sample data to construct a 90% confidence interval estimate for the proportion of the population of all people who would respond "yes" to that question. Does the confidence interval provide a good estimate of the population proportion?

HW 7.2 (9)

A physician wants to develop criteria for determining whether a patient's pulse rate is atypical, and she wants to determine whether there are significant differences between males and females. Use the sample pulse rates below. Male 96 84 88 56 68 68 60 64 60 72 Female 68 84 72 76 72 96 72 60 68 124 Click here to view a t distribution table.LOADING... Click here to view page 1 of the standard normal distribution table.LOADING... Click here to view page 2 of the standard normal distribution table.LOADING... a. Construct a 95% confidence interval estimate of the mean pulse rate for males.

HW 7.3 (10)

An IQ test is designed so that the mean is 100 and the standard deviation is 19 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with 99% confidence that the sample mean is within 6 IQ points of the true mean. Assume that σ=19 and determine the required sample size using technology. Then determine if this is a reasonable sample size for a real world calculation.

HW 7.3 (11)

Which of the following would be information in a question asking you to find the area of a region under the standard normal curve as a solution?

Hw 6.2 (25) A distance on the horizontal axis is given

In order to estimate the mean amount of time computer users spend on the internet each month, how many computer users must be surveyed in order to be 95% confident that your sample mean is within 10 minutes of the population mean? Assume that the standard deviation of the population of monthly time spent on the internet is 218 min. What is a major obstacle to getting a good estimate of the population mean? Use technology to find the estimated minimum required sample size.

HW 7.3 (12)

Using the simple random sample of weights of women from a data set, we obtain these sample statistics: n=40 and x=151.34 lb. Research from other sources suggests that the population of weights of women has a standard deviation given by σ=30.23 lb. a. Find the best point estimate of the mean weight of all women. b. Find a 95% confidence interval estimate of the mean weight of all women. Click here to view a t distribution table.LOADING... Click here to view page 1 of the standard normal distribution table.LOADING... Click here to view page 2 of the standard normal distribution table.LOADING... a. The best point estimate is nothing lb.

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Randomly selected students participated in an experiment to test their ability to determine when one minute (or sixty seconds) has passed. Forty students yielded a sample mean of 61.6 seconds. Assuming that σ=9.4 seconds, construct and interpret a 99% confidence interval estimate of the population mean of all students. Click here to view a t distribution table.LOADING... Click here to view page 1 of the standard normal distribution table.LOADING... Click here to view page 2 of the standard normal distribution table.LOADING... What is the 99% confidence interval for the population mean μ? nothing<μ<nothing (Type integers or decimals rounded to one decimal place as needed.)

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Salaries of 37 college graduates who took a statistics course in college have a mean, x, of $60,900. Assuming a standard deviation, σ, of $14,098, construct a 99% confidence interval for estimating the population mean μ. Click here to view a t distribution table.LOADING... Click here to view page 1 of the standard normal distribution table.LOADING... Click here to view page 2 of the standard normal distribution table.LOADING... $nothing<μ<$nothing (Round to the nearest integer as needed.)

HW 7.3 (15)

Use technology and the given confidence level and sample data to find the confidence interval for the population mean μ. Assume that the population does not exhibit a normal distribution. Weight lost on a diet: 90% confidence n=41 x=2.0 kg s=3.9 kg What is the confidence interval for the population mean μ?

HW 7.3 (5)

Listed below are the amounts of mercury (in parts per million, or ppm) found in tuna sushi sampled at different stores. The sample mean is 1.150 ppm and the sample standard deviation is 0.264 ppm. Use technology to construct a 90% confidence interval estimate of the mean amount of mercury in the population.

HW 7.3 (6)

A data set includes 103 body temperatures of healthy adult humans for which x=98.9°F and s=0.67°F. Complete parts (a) and (b) below. Click here to view a t distribution table.LOADING... Click here to view page 1 of the standard normal distribution table.LOADING... Click here to view page 2 of the standard normal distribution table.LOADING... a. What is the best point estimate of the mean body temperature of all healthy humans?

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In a sample of seven cars, each car was tested for nitrogen-oxide emissions (in grams per mile) and the following results were obtained: 0.08, 0.16, 0.17, 0.19, 0.06, 0.07, 0.18. Assuming that this sample is representative of the cars in use, construct a 98% confidence interval estimate of the mean amount of nitrogen-oxide emissions for all cars. If the EPA requires that nitrogen-oxide emissions be less than 0.165 g/mi, can we safely conclude that this requirement is being met? Click here to view a t distribution table.LOADING... Click here to view page 1 of the standard normal distribution table.LOADING... Click here to view page 2 of the standard normal distribution table.LOADING... What is the confidence interval estimate of the mean amount of nitrogen-oxide emissions for all cars?

HW 7.3 (8)

In a study designed to test the effectiveness of magnets for treating back pain, 35 patients were given a treatment with magnets and also a sham treatment without magnets. Pain was measured using a scale from 0 (no pain) to 100 (extreme pain). After given the magnet treatments, the 35 patients had pain scores with a mean of 6.0 and a standard deviation of 2.8. After being given the sham treatments, the 35 patients had pain scores with a mean of 5.7 and a standard deviation of 2.6. Complete parts (a) through (c) below. Click here to view a t distribution table.LOADING... Click here to view page 1 of the standard normal distribution table.LOADING... Click here to view page 2 of the standard normal distribution table.LOADING... a. Construct the 95% confidence interval estimate of the mean pain score for patients given the magnet treatment. What is the confidence interval estimate of the population mean μ?

HW 7.3 (9)

The values listed below are waiting times (in minutes) of customers at two different banks. At Bank A, customers enter a single waiting line that feeds three teller windows. At Bank B, customers may enter any one of three different lines that have formed at three teller windows. Answer the following questions.

HW 7.4 (10)

Assume that the sample is a simple random sample obtained from a normally distributed population of IQ scores of statistics professors. Use the table below to find the minimum sample size needed to be 99% confident that the sample standard deviation s is within 1% of σ. Is this sample size practical?

HW 7.4 (11)

Assume that the sample is a simple random sample obtained from a normally distributed population of flight delays at an airport. Use the table below to find the minimum sample size needed to be 99% confident that the sample standard deviation is within 5% of the population standard deviation. A histogram of a sample of those arrival delays suggests that the distribution is skewed, not normal. How does the distribution affect the sample size?

HW 7.4 (12)

Use the given information to find the number of degrees of freedom, the critical values χ2L and χ2R, and the confidence interval estimate of σ. It is reasonable to assume that a simple random sample has been selected from a population with a normal distribution. Nicotine in menthol cigarettes 90% confidence; n=24, s=0.23 mg. LOADING... Click the icon to view the table of Chi-Square critical values.

HW 7.4 (2)

Use the given information to find the number of degrees of freedom, the critical values χ2L and χ2R, and the confidence interval estimate of σ. It is reasonable to assume that a simple random sample has been selected from a population with a normal distribution. Platelet Counts of Women 98% confidence; n=24, s=65.9. LOADING... Click the icon to view the table of Chi-Square critical values.

HW 7.4 (3)

Use the given confidence level and sample data to find a confidence interval for the population standard deviation σ. Assume that a simple random sample has been selected from a population that has a normal distribution. Salaries of college professors who took a statistics course in college 90% confidence; n=71, x=$55,200, s=$16,008 LOADING... Click the icon to view the table of Chi-Square critical values.

HW 7.4 (4)

A chocolate chip cookie manufacturing company recorded the number of chocolate chips in a sample of 60 cookies. The mean is 22.15 and the standard deviation is 2.82. Construct a 99% confidence interval estimate of the standard deviation of the numbers of chocolate chips in all such cookies. LOADING... Click the icon to view the table of Chi-Square critical values.

HW 7.4 (5)

A simple random sample from a population with a normal distribution of 97 body temperatures has x=98.40°F and s=0.61°F. Construct a 99% confidence interval estimate of the standard deviation of body temperature of all healthy humans. Is it safe to conclude that the population standard deviation is less than 2.40°F? LOADING... Click the icon to view the table of Chi-Square critical values.

HW 7.4 (6)

e body mass index (BMI) for a sample of men and a sample of women are given below. Assume the samples are simple random samples obtained from populations with normal distributions. Men 25.5 24.1 31.1 26.3 32.8 31.2 28.4 32.6 23.6 26.7 Women 19.2 20.1 22.1 30.4 19.5 20.8 23.8 38.6 19.7 23.6 LOADING... Click the icon to view the table of Chi-Square critical values.

HW 7.7 (7)

Find the critical value zα/2 that corresponds to α=0.02.

HW7.2 (3)

Twelve different video games showing substance use were observed and the duration of times of game play (in seconds) are listed below. The design of the study justifies the assumption that the sample can be treated as a simple random sample. Use the sample data to construct a 90% confidence interval estimate of σ, the standard deviation of the duration times of game play. Assume that this sample was obtained from a population with a normal distribution. 4,023 4,234 4,461 4,507 4,379 4,630 4,756 4,130 5,015 3,916 4,360 4,235

HW7.4 (8)

Listed below are speeds (mi/h) measured from traffic on a busy highway. This simple random sample was obtained at 3:30 P.M. on a weekday. Use the sample data to construct a 90% confidence interval estimate of the population standard deviation.

HW7.4 (9)

Assume the readings on thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. Find the probability that a randomly selected thermometer reads greater than −1.12 and draw a sketch of the region.

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Assume that thermometer readings are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A thermometer is randomly selected and tested. For the case below, draw a sketch, and find the probability of the reading. (The given values are in Celsius degrees.)

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Assume that the readings on the thermometers are normally distributed with a mean of 0° and standard deviation of 1.00°C. A thermometer is randomly selected and tested. Draw a sketch and find the temperature reading corresponding to P87, the 87th percentile. This is the temperature reading separating the bottom 87% from the top

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Assume that a randomly selected subject is given a bone density test. Bone density test scores are normally distributed with a mean of 0 and a standard deviation of 1. Draw a graph and find P4, the 4th percentile. This is the bone density score separating the bottom 4% from the top

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Find the indicated critical value.

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Find the indicated area under the curve of the standard normal distribution, then convert it to a percentage and fill in the blank. About _____% of the area is between z=−1.1 and z=1.1 (or within 1.1 standard deviations of the mean). About 72.8672.86% of the area is between z=−1.1 and z=1.1 (or within 1.1 standard deviations of the mean). (Round to two decimal places as needed.)

Hw 6.2 (17)

Which of the following is NOT a descriptor of a normal distribution of a random variable?

Hw 6.2 (18) The graph is centered around 0.

Which of the following groups of terms can be used interchangeably when working with normal distributions?

Hw 6.2 (19) areas, probability, and relative frequencies

A continuous random variable has a _______ distribution if its values are spread evenly over the range of possibilities.

Hw 6.2 (20) uniform

Which of the following is NOT a requirement for a density curve?

Hw 6.2 (21) The graph is centered around 0.

Which of the following does NOT describe the standard normal distribution?

Hw 6.2 (22) The graph is uniform.

Finding probabilities associated with distributions that are standard normal distributions is equivalent to _______.

Hw 6.2 (23) finding the area of the shaded region representing that probability.

The notation P(z<a) denotes _______.

Hw 6.2 (24) the probability that the z-score is less than a.

Pulse rates of women are normally distributed with a mean of 77.5 beats per minute and a standard deviation of 11.6 beats per minute. Answer the following questions. What are the values of the mean and standard deviation after converting all pulse rates of women to z scores using z=(x−μ)σ a) What are the values of the mean and standard deviation after converting all pulse rates of women to z scores using z=(x−μ)σ b) The original pulse rates are measure with units of "beats per minute". What are the units of the corresponding z scores? Choose the correct choice below.

Hw 6.3 (1) u=0 o=1 The z scores are numbers without units of measurement.

Assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 15. Find the third quartile Q3, which is the IQ score separating the top 25% from the others. The third quartile, Q3, is

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survey found that women's heights are normally distributed with mean 63.4 in and standard deviation 2.5 in. A branch of the military requires women's heights to be between 58 in and 80 in. a. Find the percentage of women meeting the height requirement. Are many women being denied the opportunity to join this branch of the military because they are too short or too tall? b. If this branch of the military changes the height requirements so that all women are eligible except the shortest 1% and the tallest 2%, what are the new height requirements? Click to view page 1 of the table.LOADING... Click to view page 2 of the table.LOADING... a. The percentage of women who meet the height requirement is 98.4698.46%. (Round to two decimal places as needed.) Are many women being denied the opportunity to join this branch of the military because they are too short or too tall? No, because only a small percentage of women are not allowed to join this branch of the military because of their height. For the new height requirements, this branch of the military requires women's heights to be at least 57.657.6 in and at most 68.668.6 in.

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A survey found that women's heights are normally distributed with mean 63.1 in. and standard deviation 2.9 in. The survey also found that men's heights are normally distributed with a mean 67.4 in. and standard deviation 2.8. Complete parts a through c below. Most of the live characters at an amusement park have height requirements with a minimum of 4 ft 8 in. and a maximum of 6 ft 3 in. Find the percentage of women meeting the height requirement. The percentage of women who meet the height requirement is Find the percentage of men meeting the height requirement. The percentage of men who meet the height requirement is If the height requirements are changed to exclude only the tallest 5% of men and the shortest 5% of women, what are the new height requirements? The new height requirements are at least 58.358.3 in. and at most 7272 in.

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Men's heights are normally distributed with mean 70.1 in and standard deviation of 2.8 in. Women's heights are normally distributed with mean 63.5 in and standard deviation of 2.5 in. The standard doorway height is 80 in. a. What percentage of men are too tall to fit through a standard doorway without bending, and what percentage of women are too tall to fit through a standard doorway without bending? b. If a statistician designs a house so that all of the doorways have heights that are sufficient for all men except the tallest 5%, what doorway height would be used?

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A common design requirement is that an environment must fit the range of people who fall between the 5th percentile for women and the 95th percentile for men. In designing an assembly work table, the sitting knee height must be considered, which is the distance from the bottom of the feet to the top of the knee. Males have sitting knee heights that are normally distributed with a mean of 21.4 in. and a standard deviation of 1.1 in. Females have sitting knee heights that are normally distributed with a mean of 19.2 in. and a standard deviation of 1.0 in. Use this information to answer the following questions.

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The lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. a. Find the probability of a pregnancy lasting 307 days or longer. b. If the length of pregnancy is in the lowest 3%, then the baby is premature. Find the length that separates premature babies from those who are not premature. The probability that a pregnancy will last 307 days or longer is . 0047.0047 Babies who are born on or before 240240 days are considered premature. (Round to the nearest integer as needed.)

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Assume that human body temperatures are normally distributed with a mean of 98.19°F and a standard deviation of 0.62°F. a. A hospital uses 100.6°F as the lowest temperature considered to be a fever. What percentage of normal and healthy persons would be considered to have a fever? Does this percentage suggest that a cutoff of 100.6°F is appropriate? b. Physicians want to select a minimum temperature for requiring further medical tests. What should that temperature be, if we want only 5.0% of healthy people to exceed it? (Such a result is a false positive, meaning that the test result is positive, but the subject is not really sick.) Does this percentage suggest that a cutoff of 100.6°F is appropriate? Yes, because there is a small probability that a normal and healthy person would be considered to have a fever. The minimum temperature for requiring further medical tests should be 99.2199.21°F if we want only 5.0% of healthy people to exceed it. (Round to two decimal places as needed.)

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Assume that the Richter scale magnitudes of earthquakes are normally distributed with a mean of 1.119 and a standard deviation of 0.584. Complete parts a through c below. Earthquakes with magnitudes less than 2.000 are considered "microearthquakes" that are not felt. What percentage of earthquakes fall into this category? Earthquakes above 4.0 will cause indoor items to shake. What percentage of earthquakes fall into this category? Find the 95th percentile. D) Will all earthquakes above the 95th percentile cause indoor items to shake?

Hw 6.3 (17) D) No, because not all earthquakes above the 95th percentile have magnitudes above 4.0.

Engineers want to design seats in commercial aircraft so that they are wide enough to fit 99% of all males. (Accommodating 100% of males would require very wide seats that would be much too expensive.) Men have hip breadths that are normally distributed with a mean of 14.3 in. and a standard deviation of 1.1 in. Find P99. That is, find the hip breadth for men that separates the smallest 99% from the largest 1%. The hip breadth for men that separates the smallest 99% from the largest 1% is P99=16.916.9 in. (Round to one decimal place as needed.)

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Chocolate chip cookies have a distribution that is approximately normal with a mean of 23.8 chocolate chips per cookie and a standard deviation of 2.3 chocolate chips per cookie. Find P1 and P99. How might those values be helpful to the producer of the chocolate chip cookies?

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Find the area of the shaded region. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15. Click to view page 1 of the table.LOADING... Click to view page 2 of the table.LOADING... The area of the shaded region is

Hw 6.3 (2)

Which of the following is not true?

Hw 6.3 (20) A z-score is an area under the normal curve.

Where would a value separating the top 15% from the other values on the graph of a normal distribution be found?

Hw 6.3 (21) the right side of the horizontal scale of the graph

What conditions would produce a negative z-score?

Hw 6.3 (22) a z-score corresponding to an area located entirely in the left side of the curve

f you are asked to find the 85th percentile, you are being asked to find _____.

Hw 6.3 (23) a data value associated with an area of 0.85 to its left

Find the area of the shaded region. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15. The area of the shaded region is . 7495.7495

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Find the area of the shaded region. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15. 102 The area of the shaded region is 0.4160.416

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Find the indicated IQ score. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15. The indicated IQ score, x, is 110.2110.2

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Assume that adults have IQ scores that are normally distributed with a mean of μ=100 and a standard deviation σ=20. Find the probability that a randomly selected adult has an IQ less than 120. The probability that a randomly selected adult has an IQ less than 120 is

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Assume that adults have IQ scores that are normally distributed with a mean of μ=100 and a standard deviation σ=15. Find the probability that a randomly selected adult has an IQ between 89 and 111. Click to view page 1 of the table.LOADING... Click to view page 2 of the table.LOADING... The probability that a randomly selected adult has an IQ between 89 and 111 is . 5346.5346. (Type an integer or decimal rounded to four decimal places as needed.)

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Assume that adults have IQ scores that are normally distributed with a mean of 105 and a standard deviation 15. Find P3, which is the IQ score separating the bottom 3% from the top 97%. Click to view page 1 of the table.LOADING... Click to view page 2 of the table.LOADING... The IQ score that separates the bottom 3% from the top 97% is P3=76.876.8. (Round to the nearest hundredth as needed.)

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Which of the following statistics are unbiased estimators of population parameters?

Hw 6.4 (1) 1. Sample proportion used to estimate a population proportion. 2. Sample mean used to estimate a population mean. 3. Sample variance used to estimate a population variance.

genetics experiment involves a population of fruit flies consisting of 1 male named Albert and 3 females named Barbara, Courtney, and Dana. Assume that two fruit flies are randomly selected with replacement. Is the mean of the sampling distribution [from part (b)] equal to the population proportion of females? If so, does the mean of the sampling distribution of proportions always equal the population proportion?

Hw 6.4 (10) Yes, the sample mean is equal to the population proportion of females. These values are always equal, because proportion is an unbiased estimator.

is the distribution of all values of the statistic when all possible samples of the same size n are taken from the same population.

Hw 6.4 (11) The sampling distribution of a statistic

Which of the following is NOT a property of the sampling distribution of the sample mean? Choose the correct answer below.

Hw 6.4 (12) The distribution of the sample mean tends to be skewed to the right or left.

Which of the following is NOT a property of the sampling distribution of the variance? Choose the correct answer below.

Hw 6.4 (13) The distribution of sample variances tends to be a normal distribution.

is the distribution of sample proportions, with all samples having the same sample size n taken from the same population.

Hw 6.4 (14) The sampling distribution of the proportion

Which of the following is a biased estimator? That is, which of the following does not target the population parameter? Choose the correct answer below.

Hw 6.4 (15) Median

Three randomly selected households are surveyed. The numbers of people in the households are 1, 3, and 8. Assume that samples of size n=2 are randomly selected with replacement from the population of 1, 3, and 8. Listed below are the nine different samples. Complete parts (a) through (c). b. Compare the population variance to the mean of the sample variances. Choose the correct answer below. c) Do the sample variances target the value of the population variance? In general, do sample variances make good estimators of population variances? Why or why not?

Hw 6.4 (2) b) The population variance is equal to the mean of the sample variances. c) The sample variances target the population variances, therefore, sample variances make good estimators of population variances.

The value given below is discrete. Use the continuity correction and describe the region of the normal distribution that corresponds to the indicated probability. Probability of exactly 7 passengers who do not show up for a flight

Hw 6.7 (1) The area between 6.5 and 7.5

Assume a population of 3, 4, and 11. Assume that samples of size n=2 are randomly selected with replacement from the population. Listed below are the nine different samples. Complete parts a through d below. Find the standard deviation of each of the nine samples, then summarize the sampling distribution of the standard deviations in the format of a table representing the probability distribution of the distinct standard deviation values. Use ascending order of the sample standard deviations. D) Do the sample standard deviations target the value of the population standard deviation? In general, do sample standard deviations make good estimators of population standard deviations? Why or why not?

Hw 6.4 (3) D) The sample standard deviations do not target the population standard deviation, therefore, sample standard deviations are biased estimators.

Three randomly selected households are surveyed. The numbers of people in the households are 3, 4, and 11. Assume that samples of size n=2 are randomly selected with replacement from the population of 3, 4, and 11. Listed below are the nine different samples. Complete parts (a) through (c). B) Compare the population median to the mean of the sample medians. Choose the correct answer below. C) Do the sample medians target the value of the population median? In general, do sample medians make good estimators of population medians? Why or why not?

Hw 6.4 (4) B) The population median is not equal to the mean of the sample medians (it is also not half or double the mean of the sample medians). C) The sample medians do not target the population median, so sample medians do not make good estimators of population medians.

Three randomly selected households are surveyed. The numbers of people in the households are 1, 3, and 8. Assume that samples of size n=2 are randomly selected with replacement from the population of 1, 3, and 8. Construct a probability distribution table that describes the sampling distribution of the proportion of odd numbers when samples of sizes n=2 are randomly selected. Does the mean of the sample proportions equal the proportion of odd numbers in the population? Do the sample proportions target the value of the population proportion? Does the sample proportion make a good estimator of the population proportion? Listed below are the nine possible samples. C) Choose the correct answer below. D) Choose the correct answer below.

Hw 6.4 (5) C) The proportion of odd numbers in the population is equal to the mean of the sample proportions. D) The sample proportions target the proportion of odd numbers in the population, so sample proportions make good estimators of the population proportion.

The assets (in billions of dollars) of the four wealthiest people in a particular country are 44, 35, 17, 15. Assume that samples of size n=2 are randomly selected with replacement from this population of four values. a. After identifying the 16 different possible samples and finding the mean of each sample, construct a table representing the sampling distribution of the sample mean. In the table, values of the sample mean that are the same have been combined.

Hw 6.4 (6)

Assume a population of 48, 52, 54, and 57. Assume that samples of size n=2 are randomly selected with replacement from the population. Listed below are the sixteen different samples. Complete parts (a) through Find the median of each of the sixteen samples, then summarize the sampling distribution of the medians in the format of a table representing the probability distribution of the distinct median values. Use ascending order of the sample medians.

Hw 6.4 (7)

The ages (years) of three government officials when they died in office were 55, 46, and 60. Complete parts (a) through (d) Assuming that 2 of the ages are randomly selected with replacement, list the different possible sampl C) Compare the population range to the mean of the sample ranges. Choose the correct answer below. D) Do the sample ranges target the value of the population range? In general, do sample ranges make good estimators of population ranges? Why or why not?

Hw 6.4 (8) C) The population range is not equal to the mean of the sample ranges (it is also not equal to the age of the oldest official or age of the youngest official at the time of death). D) The sample ranges do not target the population range, therefore, sample ranges do not make good estimators of population ranges.

When two births are randomly selected, the sample space for genders is bb, bg, gb, and gg. Assume that those four outcomes are equally likely. Construct a table that describes the sampling distribution of the sample proportion of girls from two births. Does the mean of the sample proportions equal the proportion of girls in two births? Does the result suggest that a sample proportion is an unbiased estimator of a population proportion? For the entire population, assume the probability of having a boy is 12, the probability of having a girl is 12, and this is not affected by how many boys or girls have previously been born.

Hw 6.4 (9)

An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 130 lb and 181 lb. The new population of pilots has normally distributed weights with a mean of 135 lb and a standard deviation of 33.7 lb. Click here to view page 1 of the standard normal distribution.LOADING... Click here to view page 2 of the standard normal distribution.LOADING... a. If a pilot is randomly selected, find the probability that his weight is between 130 lb and 181 lb. The probability is approximately 0.47270.4727. (Round to four decimal places as needed.) b. If 31 different pilots are randomly selected, find the probability that their mean weight is between 130 lb and 181 lb. The probability is approximately . 7966.7966. (Round to four decimal places as needed.) c. When redesigning the ejection seat, which probability is more relevant?

Hw 6.5 (10) Part (a) because the seat performance for a single pilot is more important.

Use the given data values (height in inches of players in the starting lineup of a particular basketball team) and identify the corresponding z scores that are used for a normal quantile plot, then construct the normal quantile plot and determine whether the data appear to be from a population with a normal distribution. Do the data come from a normally distributed population?

Hw 6.6 (8) Yes. The pattern of the points is reasonably close to a straight line.

Use the sample data and confidence level given below to complete parts (a) through (d). A research institute poll asked respondents if they acted to annoy a bad driver. In the poll, n=2617, and x=1171 who said that they honked. Use a 99% confidence level. Find the best point estimate of the population proportion p. Write a statement that correctly interprets the confidence interval. Choose the correct answer below.

Hw 7.2 (7)

A boat capsized and sank in a lake. Based on an assumption of a mean weight of 132 lb, the boat was rated to carry 50 passengers (so the load limit was 6,600 lb). After the boat sank, the assumed mean weight for similar boats was changed from 132 lb to 170 lb. Complete parts a and b below. a. Assume that a similar boat is loaded with 50 passengers, and assume that the weights of people are normally distributed with a mean of 182.1 lb and a standard deviation of 37.7 lb. Find the probability that the boat is overloaded because the 50 passengers have a mean weight greater than 132 lb. The probability is 11. (Round to four decimal places as needed.) b. The boat was later rated to carry only 13 passengers, and the load limit was changed to 2,210 lb. Find the probability that the boat is overloaded because the mean weight of the passengers is greater than 170 (so that their total weight is greater than the maximum capacity of 2,210 lb). The probability is . 877.877. (Round to four decimal places as needed.) Do the new ratings appear to be safe when the boat is loaded with 13 passengers? Choose the correct answer below.

Hw 6.5 (11) Because there is a high probability of overloading, the new ratings do not appear to be safe when the boat is loaded with 13 passengers.

An airliner carries 250 passengers and has doors with a height of 70 in. Heights of men are normally distributed with a mean of 69.0 in and a standard deviation of 2.8 in. Complete parts (a) through (d). a. If a male passenger is randomly selected, find the probability that he can fit through the doorway without bending. The probability is . 6406.6406. (Round to four decimal places as needed.) b. If half of the 250 passengers are men, find the probability that the mean height of the 125 men is less than 70 in. The probability is 11. (Round to four decimal places as needed.) c. When considering the comfort and safety of passengers, which result is more relevant: the probability from part (a) or the probability from part (b)? Why?

Hw 6.5 (12)

Before every flight, the pilot must verify that the total weight of the load is less than the maximum allowable load for the aircraft. The aircraft can carry 37 passengers, and a flight has fuel and baggage that allows for a total passenger load of 5,994 lb. The pilot sees that the plane is full and all passengers are men. The aircraft will be overloaded if the mean weight of the passengers is greater than 5,994 lb37=162 lb. What is the probability that the aircraft is overloaded? Should the pilot take any action to correct for an overloaded aircraft? Assume that weights of men are normally distributed with a mean of 183.2 lb and a standard deviation of 35.9.

Hw 6.5 (13)

tells us that for a population with any distribution, the distribution of the sample means approaches a normal distribution as the sample size increases.

Hw 6.5 (14) Central Limit Theorem

The standard deviation of the distribution of sample means is

Hw 6.5 (15) o/sq(n)

Which of the following is NOT a conclusion of the Central Limit Theorem? Choose the correct answer below.

Hw 6.5 (16) The distribution of the sample data will approach a normal distribution as the sample size increases.

states that if, under a given assumption, the probability of a particular observed event is exceptionally small (such as less than 0.05), we conclude that the assumption is probably not correct.

Hw 6.5 (17)

Which of the following is not a commonly used practice? Choose the correct answer below.

Hw 6.5 (18) If the distribution of the sample means is normally distributed, and n>30, then the population distribution is normally distributed.

Assume that women's heights are normally distributed with a mean given by μ=63.1 in, and a standard deviation given by σ=2.9 in. (a) If 1 woman is randomly selected, find the probability that her height is less than 64 in. (b) If 39 women are randomly selected, find the probability that they have a mean height less than 64 in.

Hw 6.5 (2)

The overhead reach distances of adult females are normally distributed with a mean of 205 cm and a standard deviation of 7.8 cm. a. Find the probability that an individual distance is greater than 218.40 cm. b. Find the probability that the mean for 20 randomly selected distances is greater than 202.80 cm. c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?

Hw 6.5 (3)

Assume that women's heights are normally distributed with a mean given by μ=63.9 in, and a standard deviation given by σ=1.8 in. Complete parts a and b.

Hw 6.5 (4)

The capacity of an elevator is 15 people or 2310 pounds. The capacity will be exceeded if 15 people have weights with a mean greater than 2310/15=154 pounds. Suppose the people have weights that are normally distributed with a mean of 164 lb and a standard deviation of 29 lb. a. Find the probability that if a person is randomly selected, his weight will be greater than 154 pounds. The probability is approximately . 6331.6331. (Round to four decimal places as needed.) b. Find the probability that 15 randomly selected people will have a mean that is greater than 154 pounds. The probability is approximately . 9099.9099. (Round to four decimal places as needed.) c. Does the elevator appear to have the correct weight limit? Why or why not?

Hw 6.5 (5)

Women have head circumferences that are normally distributed with a mean given by μ=21.94 in., and a standard deviation given by σ=0.8 in. Complete parts a through c below. If this probability is high, does it suggest that an order of 6 hats will very likely fit each of 6 randomly selected women? Why or why not?

Hw 6.5 (6) No, the hats must fit individual women, not the mean from 6 women. If all hats are made to fit head circumferences between 21.7 in. and 22.7 in., the hats won't fit about half of those women.

A sample of human brain volumes (cm3) is given below. Use the given data values to identify the corresponding z scores that are used for a normal quantile plot. Then identify the coordinates of each point and use them to construct the normal quantile plot. Determine whether the data appear to be from a population with a normal distribution. A) Do the data appear to come from a normally distributed population?

Hw 6.6 (9) No, because the points in the normal quantile plot do not lie reasonably close to a straight line or show a systematic pattern that is a straight line pattern.

The weights of a certain brand of candies are normally distributed with a mean weight of 0.8551 g and a standard deviation of 0.0521 g. A sample of these candies came from a package containing 449 candies, and the package label stated that the net weight is 383.3 g. (If every package has 449 candies, the mean weight of the candies must exceed 383.3449=0.8536 g for the net contents to weigh at least 383.3 g.) a. If 1 candy is randomly selected, find the probability that it weighs more than 0.8536 g. The probability is . 5120.5120. (Round to four decimal places as needed.) b. If 449 candies are randomly selected, find the probability that their mean weight is at least 0.8536 g. The probability that a sample of 449 candies will have a mean of 0.8536 g or greater is . 7257.7257. (Round to four decimal places as needed.) c. Given these results, does it seem that the candy company is providing consumers with the amount claimed on the label? Yes, because the probability of getting a sample mean of 0.8536 g or greater when 449 candies are selected is not exceptionally small.

Hw 6.5 (7)

A ski gondola carries skiers to the top of a mountain. It bears a plaque stating that the maximum capacity is 16 people or 2576 lb. That capacity will be exceeded if 16 people have weights with a mean greater than 2576 lb16=161 lb. Assume that weights of passengers are normally distributed with a mean of 180.8 lb and a standard deviation of 43 lb. Complete parts a through c below. Does the gondola appear to have the correct weight limit? Why or why not?

Hw 6.5 (8) No, there is a high probability that the gondola will be overloaded if it is occupied by 16 passengers, so it appears that the number of allowed passengers should be reduced.

Women have pulse rates that are normally distributed with a mean of 74.4 beats per minute and a standard deviation of 11.6 beats per minute. Complete parts a through c below. a. Find the percentiles P1 and P99. P1=47.447.4 beats per minute (Round to one decimal place as needed.) P99=101.4101.4 beats per minute (Round to one decimal place as needed.) b. A doctor sees exactly 40 patients each day. Find the probability that 40 randomly selected women have a mean pulse rate between 59 and 89 beats per minute. The probability is 11. (Round to four decimal places as needed.) c. If the doctor wants to select pulse rates to be used as cutoff values for determining when further tests should be required, which pulse rates are better to use: the results from part (a) or the pulse rates of 59 and 89 beats per minute from part (b)? Why?

Hw 6.5 (9) Part (a), because the cutoff values should be based on individual patients rather than the mean pulse rate of the sample.

If you select a simple random sample of M&M plain candies and construct a normal quantile plot of their weights, what pattern would you expect in the graphs? Choose the correct answer below.

Hw 6.6 (1) Approximately a straight line.

The heights (in inches) of men listed in the accompanying table have a distribution that is approximately normal, so it appears that those heights are from a normally distributed population. Complete parts (a) through (c). A) If 1 inch is subtracted from each height, are the new heights also normally distributed? B) If each height is converted from inches to millimeters, are the heights in millimeters also normally distributed? C) Are the logarithms of normally distributed heights also normally distributed?

Hw 6.6 (10) A) Yes B) Yes C) No

Which of the following is NOT a procedure for determining whether it is reasonable to assume that sample data are from a normally distributed population? Choose the correct answer below.

Hw 6.6 (11) Checking that the probability of an event is 0.05 or less

is a graph of points (x,y) where each x-value is from the original set of sample data, and each y-value is the corresponding z-score that is a quantile value expected from the standard normal distribution.

Hw 6.6 (12) normal quantile plot

Which of the following is NOT true in regards to using a normal quantile plot to determine whether or not a distribution is normal? Choose the correct answer below.

Hw 6.6 (13) If the plot is bell-shaped, the population distribution is normal.

The normal quantile plot shown to the right represents duration times (in seconds) of eruptions of a certain geyser from the accompanying data set. Examine the normal quantile plot and determine whether it depicts sample data from a population with a normal distribution. LOADING... Click the icon to view the data set.

Hw 6.6 (2) The distribution is not normal. The points are not reasonably close to a straight line.

Examine the normal quantile plot and determine whether it depicts sample data from a population with a normal distribution.

Hw 6.6 (3) No. The points exhibit some systematic pattern that is not a straight-line pattern.

Sample data for the arrival delay times (in minutes) of airlines flights is given below. Determine whether they appear to be from a population with a normal distribution. Assume that this requirement is loose in the sense that the population distribution need not be exactly normal, but it must be a distribution that is roughly bell-shaped.

Hw 6.6 (4) No, because the histogram of the data is not bell shaped, there is more than one outlier, and the points in the normal quantile plot do not lie reasonably close to a straight line.

Refer to the data set below (body mass index of men) and determine whether the requirement of a normal distribution is satisfied. Assume that this requirement is loose in the sense that the population distribution need not be exactly normal, but it must be a distribution that is basically symmetric with only one mode.

Hw 6.6 (5) Yes. The points in the normal quantile plot lie reasonably close to a straight line.

e a calculator or computer software to generate a normal quantile plot for the data in the accompanying table. Then determine whether the data come from a normally distributed population. A) Determine whether the data come from a normally distributed population. Choose the correct answer below.

Hw 6.6 (6) The distribution is not normal. The points show a systematic pattern that is not a straight-line pattern.

A random sample of male systolic blood pressure values is given below. Generate the normal quantile plot for this data set and determine whether or not the data come from a normally distributed population. A) Do the data appear to come from a normally distributed population?

Hw 6.6 (7) A) Yes, because the pattern of the points in the normal quantile plot is reasonably close to a straight line.

A gender-selection technique is designed to increase the likelihood that a baby will be a girl. In the results of the gender-selection technique, 851 births consisted of 435 baby girls and 416 baby boys. In analyzing these results, assume that boys and girls are equally likely. a. Find the probability of getting exactly 435 girls in 851 births. b. Find the probability of getting 435 or more girls in 851 births. If boys and girls are equally likely, is 435 girls in 851 births unusually high? c. Which probability is relevant for trying to determine whether the technique is effective: the result from part (a) or the result from part (b)? d. Based on the results, does it appear that the gender-selection technique is effective?

Hw 6.7 (10)

Assume 44% of us have Group O blood. A hospital is conducting a blood drive because its supply of Group O blood is low, and it needs at least 148 donors of Group O blood. If 334 volunteers donate blood, estimate the probability that the number with Group O blood is at least 148. Is the pool of 334 volunteers likely to be sufficient? A) What does the result from part (a) suggest?

Hw 6.7 (11) The pool is not likely to be sufficient because P(x≥148) is less than 50%.

In a survey of 1273 people, 903 people said they voted in a recent presidential election. Voting records show that 68% of eligible voters actually did vote. Given that 68% of eligible voters actually did vote, (a) find the probability that among 1273 randomly selected voters, at least 903 actually did vote. (b) What do the results from part (a) suggest?

Hw 6.7 (12)

In a study of 308,781 cell phone users, it was found that 53 developed cancer of the brain or nervous system. Assuming that cell phones have no effect, there is a 0.000177 probability of a person developing cancer of the brain or nervous system. We therefore expect about 55 cases of such cancer in a group of 308,781 people. Estimate the probability of 53 or fewer cases of such cancer in a group of 308,781 people. What do these results suggest about media reports that cell phones cause cancer of the brain or nervous system?

Hw 6.7 (13)

Based on a recent survey, 30% of adults in a specific country smoke. In a survey of 80 students, it is found that 21 of them smoke. Find the probability that should be used for determining whether the 30% rate is correct for students. What can be concluded?

Hw 6.7 (14)

Which of the following is NOT a requirement for using the normal distribution as an approximation to the binomial distribution?

Hw 6.7 (15) The sample is the result of conducting several dependent trials of an experiment in which the probability of success is p.

Why must a continuity correction be used when using the normal approximation for the binomial distribution? Choose the correct answer below.

Hw 6.7 (16) The normal distribution is a continuous probability distribution being used as an approximation to the binomial distribution which is a discrete probability distribution.

Which statement below indicates the area to the left of 19.5 before a continuity correction is used? Choose the correct answer below.

Hw 6.7 (17) At most 19

Which is NOT a criterion for distinguishing between results that could easily occur by chance and those results that are highly unusual? Choose the correct answer below.

Hw 6.7 (18) the sample size is less than 5% of the size of the population

If np≥5 and nq≥5, estimate P(fewer than 5) with n=13 and p=0.6 by using the normal distribution as an approximation to the binomial distribution; if np<5 or nq<5, then state that the normal approximation is not suitable.

Hw 6.7 (2)

If np≥5 and nq≥5, estimate P(more than 6) with n=11 and p=0.4 by using the normal distribution as an approximation to the binomial distribution; if np<5 or nq<5, then state that the normal approximation is not suitable.

Hw 6.7 (3)

If np≥5 and nq≥5, estimate P(at least 5) with n=13 and p=0.6 by using the normal distribution as an approximation to the binomial distribution; if np<5 or nq<5, then state that the normal approximation is not suitable.

Hw 6.7 (4)

Use a normal approximation to find the probability of the indicated number of voters. In this case, assume that 121 eligible voters aged 18-24 are randomly selected. Suppose a previous study showed that among eligible voters aged 18-24, 22% of them voted. Probability that fewer than 29 voted

Hw 6.7 (5)

Use a normal approximation to find the probability of the indicated number of voters. In this case, assume that 147 eligible voters aged 18-24 are randomly selected. Suppose a previous study showed that among eligible voters aged 18-24, 22% of them voted. Probability that exactly 36 voted

Hw 6.7 (6)

A scientist conducted a hybridization experiment using peas with green pods and yellow pods. He crossed peas in such a way that 25% (or 148) of the 592 offspring peas were expected to have yellow pods. Instead of getting 148 peas with yellow pods, he obtained 151. Assume that the rate of 25% is correct. a. Find the probability that among the 592 offspring peas, exactly 151 have yellow pods. b. Find the probability that among the 592 offspring peas, at least 151 have yellow pods. c. Which result is useful for determining whether the claimed rate of 25% is incorrect? (Part (a) or part (b)?) d. Is there strong evidence to suggest that the rate of 25% is incorrect?

Hw 6.7 (7)

A scientist conducted a hybridization experiment using peas with green pods and yellow pods. He crossed peas in such a way that 25% (or 138) of the 552 offspring peas were expected to have yellow pods. Instead of getting 138 peas with yellow pods, he obtained 142. Assume that the rate of 25% is correct. a. Find the probability that among the 552 offspring peas, exactly 142 have yellow pods. b. Find the probability that among the 552 offspring peas, at least 142 have yellow pods. c. Which result is useful for determining whether the claimed rate of 25% is incorrect? (Part (a) or part (b)?) d. Is there strong evidence to suggest that the rate of 25% is incorrect?

Hw 6.7 (8)

Can we safely conclude that the requirement that nitrogen-oxide emissions be less than 0.165 g/mi is being met?

No, it is possible that the requirement is being met, but it is also very possible that the mean is not less than 0.165 g/mi.

The probability of flu symptoms for a person not receiving any treatment is 0.049. In a clinical trial of a common drug used to lower cholesterol, 46 of 865 people treated experienced flu symptoms. Assuming the drug has no effect on the likelihood of flu symptoms, estimate the probability that at least 46 people experience flu symptoms. What do these results suggest about flu symptoms as an adverse reaction to the drug? A) What does the result from part (a) suggest?

Hw 6.7 (9) A) The drug has no effect on flu symptoms because x≥46 is not highly unlikely.

A newspaper provided a "snapshot" illustrating poll results from 1910 professionals who interview job applicants. The illustration showed that 26% of them said the biggest interview turnoff is that the applicant did not make an effort to learn about the job or the company. The margin of error was given as ±3 percentage points. What important feature of the poll was omitted?

Hw 7.2 (1) The confidence level

Use the data in the table to the right to answer the following questions. Find the sample proportion of candy that are red. The proportion of red candy=

Hw 7.2 (10)

During a period of 11 years 1500 of the people selected for grand jury duty were sampled, and 35% of them were immigrants. Use the sample data to construct a 99% confidence interval estimate of the proportion of grand jury members who were immigrants. Given that among the people eligible for jury duty, 57.4% of them were immigrants, does it appear that the jury selection process was somehow biased against immigrants? Does it appear that the jury selection process was somehow biased against immigrants?

Hw 7.2 (11) Yes, the confidence interval does not include the true percentage of immigrants.

Use the given data to find the minimum sample size required to estimate a population proportion or percentage. Margin of error: 0.07; confidence level 90%; p and q unknown

Hw 7.2 (12)

Many states are carefully considering steps that would help them collect sales taxes on items purchased through the Internet. How many randomly selected sales transactions must be surveyed to determine the percentage that transpired over the Internet? Assume that we want to be 90% confident that the sample percentage is within seven percentage points of the true population percentage for all sales transactions.

Hw 7.2 (13)

Find the sample size, n, needed to estimate the percentage of adults who have consulted fortune tellers. Use a 0.04 margin of error, use a confidence level of 95%, and use results from a prior poll suggesting that 10% of adults have consulted fortune tellers.

Hw 7.2 (14)

A programmer plans to develop a new software system. In planning for the operating system that he will use, he needs to estimate the percentage of computers that use a new operating system. How many computers must be surveyed in order to be 90% confident that his estimate is in error by no more than two percentage points? Complete parts (a) through (c) below.

Hw 7.2 (15)

The brand manager for a brand of toothpaste must plan a campaign designed to increase brand recognition. He wants to first determine the percentage of adults who have heard of the brand. How many adults must he survey in order to be 90% confident that his estimate is within six percentage points of the true population percentage? Complete parts (a) through (c) below. Given that the required sample size is relatively small, could he simply survey the adults at the nearest college?

Hw 7.2 (16) No, a sample of students at the nearest college is a convenience sample, not a simple random sample, so it is very possible that the results would not be representative of the population of adults.

Which concept below is NOT a main idea of estimating a population proportion? Choose the correct answer below.

Hw 7.2 (18) Using a sample statistic to estimate the population proportion is utilizing descriptive statistics.

Which of the following groups has terms that can be used interchangeably with the others? Choose the correct answer below.

Hw 7.2 (19) Percentage, Probability, and Proportion

Find the critical value zα/2 that corresponds to the given confidence level.

Hw 7.2 (2)

A _______ is a single value used to approximate a population parameter.

Hw 7.2 (20) point estimate

Which of the following is NOT true of the confidence level of a confidence interval? Choose the correct answer below.

Hw 7.2 (21) There is a 1−α chance, where α is the complement of the confidence level, that the true value of p will fall in the confidence interval produced from our sample.

Which of the following is NOT an observation about critical values? Choose the correct answer below.

Hw 7.2 (22) A critical value is the area in the right-tail region of the standard normal curve.

Which of the following is NOT a requirement for constructing a confidence interval for estimating the population proportion? Choose the correct answer below.

Hw 7.2 (23) The trials are done without replacement.

When analyzing polls, which of the following is NOT a consideration? Choose the correct answer below.

Hw 7.2 (24) The sample should be a voluntary response or convenience sample.

Which of the following is NOT needed to determine the minimum sample size required to estimate a population proportion? Choose the correct answer below.

Hw 7.2 (25) Standard Deviation

Find the critical value zα/2 that corresponds to α=0.02.

Hw 7.2 (3)

Express the confidence interval 0.222<p<0.888 in the form p±E.

Hw 7.2 (4)

Express the confidence interval (0.079,0.125) in the form of p−E<p<p+E.

Hw 7.2 (5)

Use the sample data and confidence level given below to complete parts (a) through (d). A research institute poll asked respondents if they felt vulnerable to identity theft. In the poll, n=1036 and x=540 who said "yes." Use a 95% confidence level. Find the best point estimate of the population proportion p. 0.521 Identify the value of the margin of error E. Write a statement that correctly interprets the confidence interval. Choose the correct answer below.

Hw 7.2 (6)

In the week before and the week after a holiday, there were 10,000 total deaths, and 4985 of them occurred in the week before the holiday. a. Construct a 95% confidence interval estimate of the proportion of deaths in the week before the holiday to the total deaths in the week before and the week after the holiday. b. Based on the result, does there appear to be any indication that people can temporarily postpone their death to survive the holiday?

Hw 7.2 (8)

Hw 7.2 (9)

The population of current statistics students has ages with mean μ and standard deviation σ. Samples of statistics students are randomly selected so that there are exactly 45 students in each sample. For each sample, the mean age is computed. What does the central limit theorem tell us about the distribution of those mean ages?

Hw.6.5 (1) Because n>30, the sampling distribution of the mean ages can be approximated by a normal distribution with mean μ and standard deviation σ45.

What is a major obstacle to getting a good estimate of the population mean?

It is difficult to precisely measure the amount of time spent on the internet, invalidating some data values.

Do the confidence interval limits contain 98.6°F?

Is there strong evidence to suggest that the rate of 25% is incorrect?

If this probability is high, does it suggest that an order of 11 hats will very likely fit each of 11 randomly selected women? Why or why not?

No, the hats must fit individual women, not the mean from 11 women. If all hats are made to fit head circumferences between 20.1 in. and 21.1 in., the hats won't fit about half of those women.

Does the gondola appear to have the correct weight limit? Why or why not?

No, there is a high probability that the gondola will be overloaded if it is occupied by 16 passengers, so it appears that the number of allowed passengers should be reduced.

Does the confidence interval describe the standard deviation for all times during the week? Choose the correct answer below.

No. The confidence interval is an estimate of the standard deviation of the population of speeds at 3:30 on a weekday, not other times.

The statistics of n=22 and s=14.3 result in this 95% confidence interval estimate of σ: 11.0<σ<20.4. That confidence interval can also be expressed as (11.0, 20.4). Given that 15.7±4.7 results in values of 11.0 and 20.4, can the confidence interval be expressed as 15.7±4.7 as well?

No. The format implies that s=15.7, but s is given as 14.3. In general, a confidence interval for σ does not have s at the center.

Based on the result, does there appear to be any indication that people can temporarily postpone their death to survive the holiday?

No, because the proportion could easily equal 0.5. The interval is not less than 0.5 the week before the holiday.

Is this sample size practical?

No, because the sample size is excessively large to be practical for most applications. or Yes, because the sample size is small enough to be practical for most applications.

Write a statement that correctly interprets the confidence interval. Choose the correct answer below.

One has 95% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion.

When redesigning the ejection seat, which probability is more relevant?

Part (a) because the seat performance for a single pilot is more important.

If the doctor wants to select pulse rates to be used as cutoff values for determining when further tests should be required, which pulse rates are better to use: the results from part (a) or the pulse rates of 64 and 88 beats per minute from part (b)? Why?

Part (a), because the cutoff values should be based on individual patients rather than the mean pulse rate of the sample.

When considering the comfort and safety of passengers, why are women ignored in this case?

Since men are generally taller than women, a design that accommodates a suitable proportion of men will necessarily accommodate a greater proportion of women.

Compare the results. Does the treatment with magnets appear to be effective?

Since the confidence intervals overlap, it appears that the magnet treatments are no more effective than the sham treatments.

Compare and interpret the results.

Since the intervals overlap, the populations appear to have amounts of variation that are not substantially different.

What does the result from part (a) suggest?

Some people are being less than honest because P(x≥1003) is less than 5%.

Which of the following is NOT needed to determine the minimum sample size required to estimate a population proportion?

Standard Deviation

What area under the normal distribution corresponds to the probability that a pilot's weight is between 140 lb and 201 lb?

The area between z=−0.24 and z=1.58.

What area under the normal distribution curve corresponds to the probability that a woman's head circumference is between 20.6 in. and 21.6 in.?

The area between z=−0.54 and z=0.71.

What area should be determined to find the probability that a woman's height is less than 64 in?

The area under the normal distribution and to the left of z=0.23.

A histogram of a sample of those arrival delays suggests that the distribution is skewed, not normal. How does the distribution affect the sample size?

The computed minimum sample size is not likely correct.

What does it mean to say that the confidence interval methods of this section are robust against departures from normality?

The confidence interval methods of this section are robust against departures from normality, meaning they work well with distributions that aren't normal, provided that departures from normality are not too extreme.

The confidence level

Which of the following is NOT a requirement for constructing a confidence interval for estimating a population mean with σ known?

The confidence level is 95%.

What does the result from part (a) suggest?

The drug has no effect on flu symptoms because x≥71 is not highly unlikely.

HW 6.2 (1) What requirements are necessary for a normal probability distribution to be a standard normal probability distribution?

The mean and standard deviation have the values of μ=0 and o=1

What does the result from part (a) suggest about the media reports?

The media reports appear to be incorrect because one would expect that more than 55 cell phone users would develop cancer. In fact, the study may offer some evidence to suggest that cell phone use decreases the probability of developing cancer.

Choose the correct answer below.

The normal distribution can be used because the original population has a normal distribution.

What does the result from part (a) suggest?

The pool is not likely to be sufficient because P(x≥148) is less than 50%. Your answer is correct.

Compare the population median to the mean of the sample medians. Choose the correct answer below.

The population median is not equal to the mean of the sample medians (it is also not half or double the mean of the sample medians).

Which of the following is NOT a requirement of constructing a confidence interval estimate for a population variance?

The population must be skewed to the right.

Compare the population variance to the mean of the sample variances. Choose the correct answer below.

The population variance is equal to the mean of the sample variances.

Which of the following calculations is NOT derived from the confidence interval?

The population mean, μ=(upper confidence limit)+(lower confidence limit)

When considering the comfort and safety of passengers, which result is more relevant: the probability from part (a) or the probability from part (b)? Why?

The probability from part (a) is more relevant because it shows the proportion of male passengers that will not need to bend.

Choose the correct answer below.

The proportion of odd numbers in the population is equal to the mean of the sample proportions. or The proportion of even numbers in the population is equal to the mean of the sample proportions.

Do the sample medians target the value of the population median? In general, do sample medians make unbiased estimators of population medians? Why or why not?

The sample medians do not target the population median, so sample medians are biased estimators, because the mean of the sample medians does not equal the population median.

Do the sample medians target the value of the population median? In general, do sample medians make good estimators of population medians? Why or why not?

The sample medians do not target the population median, so sample medians do not make good estimators of population medians.

Choose the correct answer below.

The sample proportions target the proportion of odd numbers in the population, so sample proportions make good estimators of the population proportion. or The sample proportions target the proportion of even numbers in the population, so sample proportions make good estimators of the population proportion.

When analyzing polls, which of the following is NOT a consideration?

The sample should be a voluntary response or convenience sample.

Do the sample standard deviations target the value of the population standard deviation? In general, do sample standard deviations make good estimators of population standard deviations? Why or why not?

The sample standard deviations do not target the population standard deviation, therefore, sample standard deviations are biased estimators.

Do the sample variances target the value of the population variance? In general, do sample variances make good estimators of population variances? Why or why not?

The sample variances target the population variances, therefore, sample variances make good estimators of population variances.

Which of the following is NOT required to determine minimum sample size to estimate a population mean?

The size of the population, N

Which of the following is NOT a property of the Student t distribution?

The standard deviation of the Student t distribution is s=1.

Determine if the following statement is true or false. If there is clearance for 95% of males, there will certainly be clearance for all women in the bottom 5%.

The statement is true because the 95th percentile for men is greater than the 5th percentile for women.

Which of the following is NOT a requirement for constructing a confidence interval for estimating the population proportion?

The trials are done without replacement.

Interpret the results found in the previous parts. Do the confidence intervals suggest a difference in the variation among waiting times? Does the single-line system or the multiple-line system seem to be a better arrangement?

The variation appears to be significantly lower with a single line system. The single-line system appears to be better.

Which of the following is NOT true of the confidence level of a confidence interval?

There is a 1−α chance, where α is the complement of the confidence level, that the true value of p will fall in the confidence interval produced from our sample.

What can be concluded?

There is not very strong evidence against the 30% rate because this probability is not very small.

Is it safe to conclude that the population standard deviation is less than 0.90°F?

This conclusion is safe because 0.90°F is outside the confidence interval.

What does this suggest about the use of 98.6°F as the mean body temperature?

This suggests that the mean body temperature could be higher than 98.6°F.

Which concept below is NOT a main idea of estimating a population proportion? Choose the correct answer below.

Using a sample statistic to estimate the population proportion is utilizing descriptive statistics.

Which of the following would be a correct interpretation of a 99% confidence interval such as 4.1<μ<5.6?

We are 99% confident that the interval from 4.1 to 5.6 actually does contain the true value of μ.

Would it be reasonable to sample this number of students?

Yes This number of IQ test scores is a fairly small number.

Does the given dotplot appear to satisfy these requirements?

Yes, because the dotplot resembles a normal distribution and the sample size is greater than 30.

Does the result suggest that a sample proportion is an unbiased estimator of a population proportion?

Yes, because the sample proportions and the population proportion are the same.

Is the mean of the sampling distribution [from part (b)] equal to the population proportion of males? If so, does the mean of the sampling distribution of proportions always equal the population proportion?

Yes, the sample mean is equal to the population proportion of males. These values are always equal, because proportion is an unbiased estimator.

Does the additional survey information from part (b) have much of an effect on the sample size that is required?

Yes, using the additional survey information from part (b) dramatically reduces the sample size.

Should the pilot take any action to correct for an overloaded aircraft?

Yes. Because the probability is high, the pilot should take action by somehow reducing the weight of the aircraft.

Based on the result, is it likely that the students' estimates have a mean that is reasonably close to sixty seconds?

Yes, because the confidence interval includes sixty seconds.

Does it appear that the jury selection process was somehow biased against immigrants?

Yes, the confidence interval does not include the true percentage of immigrants.

Is the confidence interval affected by the fact that the data appear to be from a population that is not normally distributed?

No, because the sample size is large enough.

The number of _______ for a collection of sample data is the number of sample values that can vary after certain restrictions have been imposed on all data values.

degrees of freedom

The mean of the population, 27.7527.75, is equal to the mean of the sample means, 27.7527.75. (Round to two decimal places as needed.)

equal

Does convenience sampling produce samples that are necessarily representative of the population?

A _______ is a single value used to approximate a population parameter.

point estimate

The _______ is the best point estimate of the population mean.

sample mean

The _____________ is the best point estimate of the population mean.

sample mean

The best point estimate of the population variance σ2 is the _____________.

sample variance comma s^2

Do one of the following, as appropriate. (a) Find the critical value zα/2, (b) find the critical value tα/2, (c) state that neither the normal nor the t distribution applies. Confidence level 98%; n=23; σ is unknown; population appears to be normally distributed.

t=2.508

Will all earthquakes above the 95th percentile cause indoor items to shake?

No, because not all earthquakes above the 95th percentile have magnitudes above 4.0.

Since np=8.4 and nq=5.6, is the normal distribution suitable for approximating the probability?

yes

A critical value, zα, denotes the _______.

z-score with an area of a to its right

Do one of the following, as appropriate. (a) Find the critical value zα/2, (b) find the critical value tα/2, (c) state that neither the normal nor the t distribution applies. Confidence level 99%; n=16; σ=18; population appears to be normally distributed.

z=2.575

Given that the required sample size is relatively small, could he simply survey the adults at the nearest college?

No, a sample of students at the nearest college is a convenience sample, not a simple random sample, so it is very possible that the results would not be representative of the population of adults.

Compare the preceding results. Can we conclude that the population means for males and females are different?

No, because the two confidence intervals overlap, we cannot conclude that the two population means are different.

Does the confidence interval provide a good estimate of the population proportion?

No, the sample is a voluntary sample and might not be representative of the population.

Does the elevator appear to have the correct weight limit? Why or why not?

No, there is a good chance that 15 randomly selected people will exceed the elevator capacity.

Which of the following groups has terms that can be used interchangeably with the others?

Percentage, Probability, and Proportion

Does this percentage suggest that a cutoff of 100.6°F is appropriate?

Yes, because there is a small probability that a normal and healthy person would be considered to have a fever.

Does the mean of the sample proportions equal the proportion of girls in two births?

Yes, both the mean of the sample proportions and the population proportion are 1/2.

Stats 7.2

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