stats 2381 exam 2

Suppose 3,600 healthy subjects aged 18-49 were vaccinated with a vaccine against the flu in a clinical study. Over a period of roughly 28 weeks, 24 of these subjects developed the flu. Construct the 90% confidence interval for the population proportion. (Round to four decimal places as needed.)

(0.0040, 0.0093)

In the United States, the mean birth weight for boys is 3.41 kg, with a standard deviation of 0.55 kg. Assume that the distribution of birth weight is approximately normal. What is the z-score for a baby boy that weighs 1.5 kg (defined as extremely low birth weight)? (Round to two decimal places as needed.)

-3.47

When the COVID-19 pandemic broke out in March 2020, one of the important parameters for planning how to respond to the crisis was the proportion of a country's population that was infected with the virus. Because testing for the virus was only available for those who presented with severe symptoms (tests were in short supply), the proportion of those that tested positive for the virus was not a reliable estimate for the general population because many people that contracted the virus never showed any symptoms. In an effort to estimate this proportion, one country obtained what could be treated as a representative sample. During one week in March 2020, a genetics lab in this country tested 5,507 people, of which only 48 tested positive. Construct a 95% confidence interval for the population proportion of infected people in this country around the time the testing took place. (Round to four decimal places as needed.)

(0.0063, 0.0112)

A certain website has data on thousands of cars regarding their fuel efficiency. A random sample from this website of SUVs manufactured between 2012 and 2015 gives the data in the file suv_fuel.jmp on the combined (city and highway) miles per gallon (mpg). The data file can be found on Canvas under Files. Use JMP to find a 95% confidence interval for the mean mpg for all SUVs on the website. (round to two decimal places)

(19.48, 25.52)

One feature smartphone manufacturers use in advertising is the amount of time one can continuously talk before recharging the battery. In the file talk_time.jmp are 13 values from a random sample of the talk-time (in minutes) of smartphones running on lithium-ion batteries. The file can be found under Files on Canvas. Use JMP to determine a 90% confidence interval for the population mean. (round to two decimal places)

(440.95, 674.29)

Researchers are interested in the effect of a certain nutrient on the growth rate of plant seedlings. Using a hydroponics growth procedure that utilized water containing the nutrient, they planted six tomato plants and recorded the heights of each plant 14 days after germination. Those heights, measured in millimeters, can be found in the file seedlings_height.jmp (found on Canvas under Files). Find the 99% confidence interval for the population mean.

(53.64, 71.76)

Suppose 3,600 healthy subjects aged 18-49 were vaccinated with a vaccine against the flu in a clinical study. Over a period of roughly 28 weeks, 24 of these subjects developed the flu. Find standard error of the point estimate of the population proportion that were vaccinated with the vaccine but still developed the flu. (Round to four decimal places as needed.

.0014

Suppose 3,600 healthy subjects aged 18-49 were vaccinated with a vaccine against the flu in a clinical study. Over a period of roughly 28 weeks, 24 of these subjects developed the flu. Find standard error of the point estimate of the population proportion that were vaccinated with the vaccine but still developed the flu. (Round to four decimal places as needed.)

.0014

Suppose 3,600 healthy subjects aged 18-49 were vaccinated with a vaccine against the flu in a clinical study. Over a period of roughly 28 weeks, 24 of these subjects developed the flu. Find the margin of error for a 90% confidence interval for the population proportion that were vaccinated with the vaccine but still developed the flu. (Round to four decimal places as needed.)

.0022

When the COVID-19 pandemic broke out in March 2020, one of the important parameters for planning how to respond to the crisis was the proportion of a country's population that was infected with the virus. Because testing for the virus was only available for those who presented with severe symptoms (tests were in short supply), the proportion of those that tested positive for the virus was not a reliable estimate for the general population because many people that contracted the virus never showed any symptoms. In an effort to estimate this proportion, one country obtained what could be treated as a representative sample. During one week in March 2020, a genetics lab in this country tested 5,507 people, of which only 48 tested positive. Find the margin of error for a 95% confidence interval for the population proportion of infected people in this country around the time the testing took place. (Round to four decimal places as needed.)

.0025

Suppose 3,600 healthy subjects aged 18-49 were vaccinated with a vaccine against the flu in a clinical study. Over a period of roughly 28 weeks, 24 of these subjects developed the flu. Find the point estimate of the population proportion that were vaccinated with the vaccine but still developed the flu. (Round to four decimal places as needed.)

.0067

When the COVID-19 pandemic broke out in March 2020, one of the important parameters for planning how to respond to the crisis was the proportion of a country's population that was infected with the virus. Because testing for the virus was only available for those who presented with severe symptoms (tests were in short supply), the proportion of those that tested positive for the virus was not a reliable estimate for the general population because many people that contracted the virus never showed any symptoms. In an effort to estimate this proportion, one country obtained what could be treated as a representative sample. During one week in March 2020, a genetics lab in this country tested 5,507 people, of which only 48 tested positive. Estimate the population proportion of infected people in this country around the time the testing took place. (Round to four decimal places as needed.)

.0087

You'd like to estimate the proportion of the 13,500 undergraduate students at a university who are full-time students. You poll a random sample of 350 students, of whom 322 are full-time. Unknown to you, the proportion of all undergraduate students who are full-time students is 0.928. Let X denote a random variable for which x = 0 denotes part-time students and x = 1 denotes full-time students. Find the standard deviation of the sampling distribution of the sample proportion for a sample of 350. (Round to three decimal places as needed. )

.014

Consider a sampling distribution with p = 0.15 and samples of size n=250. Using the appropriate formula, find the standard deviation of the sampling distribution of the sample proportion. (Round to four decimal places as needed.)

.0226

One question on a survey asked whether people believe in hell. 815 out of 1,138 respondents to this question answered either "Yes, definitely" or "Yes, probably." The sampling distribution of the sample proportion is approximately normal for such a large sample. Find the margin of error for this point estimate when the confidence level is 95%. (Type an integer or decimal rounded to three decimal places as needed.)

.026

In the United States, the mean birth weight for boys is 3.41 kg, with a standard deviation of 0.55 kg. Assume that the distribution of birth weight is approximately normal. A baby is considered of low birth weight if it weighs less than 2.5 kg. What proportion of baby boys in this country are born with low birth weight? (Round to three decimal places as needed.)

.0495

Using the Sampling Distribution for the Sample Proportion web app simulate an exit poll for a referendum that only allowed for a "Yes" and "No" vote. Assume the true proportion of Yes votes in the population is 0.47. Simulate 10,000 samples of size 100 at once. Use the histogram of the 10,000 sample proportions you generated to describe the variability of the sampling distribution. The sampling distribution has a standard deviation of(Round to three decimal places as needed.)

.05

Let p = 0.35 be the proportion of smart phone owners who have a given app. For a particular smart phone owner, let x = 1 if they have the app and x = 0 otherwise. For a random sample of 50 owners, find the standard deviation of the sampling distribution of the sample proportion who have the app among the 50 people. (Round to three decimal places as needed.)

.0675

You'd like to estimate the proportion of the 13,500 undergraduate students at a university who are full-time students. You poll a random sample of 350 students, of whom 322 are full-time. Unknown to you, the proportion of all undergraduate students who are full-time students is 0.928. Let X denote a random variable for which x = 0 denotes part-time students and x = 1 denotes full-time students. The population distribution has P(0)=______. (Fill in the blank. Do not round. )

.072

You'd like to estimate the proportion of the 13,500 undergraduate students at a university who are full-time students. You poll a random sample of 350 students, of whom 322 are full-time. Unknown to you, the proportion of all undergraduate students who are full-time students is 0.928. Let X denote a random variable for which x = 0 denotes part-time students and x = 1 denotes full-time students. The data distribution has P(0)=______. (Fill in the blank. Do not round. )

.08

A World Health Organization study of health in various countries reported that in Canada, systolic blood pressure readings have a mean of 121 and a standard deviation of 16. A reading above 140 is considered to be high blood pressure. If systolic blood pressure in Canada has a normal distribution, what proportion of Canadians suffers from high blood pressure? (Round to four decimal places as needed.)

.117

Consider a sampling distribution with p = 0.15 and samples of size n=1000. Using the appropriate formula, find the mean of the sampling distribution of the sample proportion.

.15

For a normal distribution, use a standard normal distribution table or technology to find the probability that an observation is at least 1 standard deviation above the mean. (Round to three decimal places as needed.)

.1587

For a normal distribution, use a standard normal distribution table or technology to find the probability that an observation is at least 1 standard deviation below the mean. (Round to three decimal places as needed.)

.1587

The Mental Development Index (MDI) of the Bayley Scales of Infant Development is a standardized measure used in observing infants over time. It is approximately normal with a mean of 100 and a standard deviation of 16. What proportion of children has an MDI of at least 115? (Round to four decimal places as needed.)

.1736

A student running for a position in student government believes that 54% of the student body will vote for her. However, she is worried about low voter turnout. Assuming she truly has 54% support in the entire student body and only n = 100 students show up for voting, how likely is it that she will not get the majority of the vote? That is, find the probability the sample proportion is 50% or lower from the 100 votes cast. (Round to four decimal places as needed.)

.2119

An energy study in Gainesville, Florida, found that in March 2006, household use of electricity had a mean of 673 and a standard deviation of 556 kilowatt-hours. Suppose the distribution of energy use was normal. Find the proportion of households with electricity use greater than 950 kilowatt-hours. (Round to four decimal places as needed.)

.3085

The random-number generator is used to generate a real number at random between 0 and 1, equally likely to fall anywhere in this interval of values. (For instance, 0.3794259382... is a possible outcome.) Find the probability that the random number is less than 0.34. (Type a decimal. Do not round.)

.34

Assume each newborn baby has a probability of approximately 0.49 of being female and 0.51 of being male. For a family with four children, let X = number of children who are girls. Find the probability that the family has two girls and two boys. (Round to four decimal places as needed.)

.3747

The table shows the probability distribution of the number of bases for a randomly selected time at bat for a random player on a certain baseball team. Find the mean of this probability distribution. (Type an integer or a decimal. Do not round.)

.4046

Using the Sampling Distribution for the Sample Proportion web app simulate an exit poll for a referendum that only allowed for a "Yes" and "No" vote. Assume the true proportion of Yes votes in the population is 0.47. Simulate 10,000 samples of size 100 at once. Use the histogram of the 10,000 sample proportions you generated to describe the center of the sampling distribution. The sampling distribution has a mean of(Round to three decimal places as needed.)

.47

The random-number generator is used to generate a real number at random between 0 and 1, equally likely to fall anywhere in this interval of values. (For instance, 0.3794259382... is a possible outcome.) What is the mean of this probability distribution? (Type a decimal. Do not round.)

.5

A student running for a position in student government believes that 54% of the student body will vote for her. However, she is worried about low voter turnout. Assuming she truly has 54% support in the entire student body, find the mean of the sampling distribution for the proportion of votes she will receive if only n = 100 students show up for voting. (Round to three decimal places as needed.)

.54

An exit poll is taken of 3,350 voters in a statewide election. Let X denote the number who voted in favor of a special proposition designed to lower property taxes and raise the sales tax. Suppose that in the population, exactly 60 % voted for it. Identify p for the binomial.

.6

Let X represent the number of homes a real estate agent sells during a given month. Based on previous sales records, she estimates that P(0) = 0.62, P(1) = 0.21, P(2) = 0.13, P(3) = 0.03, P(4) = 0.01, with negligible probability for higher values of x. Find the long-term average number of homes the real estate agent expects to sell each month.

.6

One question on a survey asked whether people believe in hell. 815 out of 1,138 respondents to this question answered either "Yes, definitely" or "Yes, probably." Find the point estimate of the population proportion who believe in hell. (Type an integer or decimal rounded to two decimal places as needed.)

.72

A World Health Organization study of health in various countries reported that in Canada, systolic blood pressure readings have a mean of 121 and a standard deviation of 16. A reading above 140 is considered to be high blood pressure. What proportion of Canadians has systolic blood pressure in the range from 104 to 140? (Round to four decimal places as needed.)

.7384

The random-number generator is used to generate a real number at random between 0 and 1, equally likely to fall anywhere in this interval of values. (For instance, 0.3794259382... is a possible outcome.) Find the probability that the random number falls between 0.25 and 1. (Type a decimal. Do not round.)

.75

An organization's survey of one country's citizens asked whether they find it acceptable for a foreign government to monitor communications from their country's leaders. Results from the survey show that of 800 citizens interviewed, 608 found it unacceptable. Find the point estimate of the population proportion of citizens of the country who find it unacceptable for a foreign government to monitor communications from their country's leaders. (Round to two decimal places as needed.

.76

An organization's survey of one country's citizens asked whether they find it acceptable for a foreign government to monitor communications from their country's leaders. Results from the survey show that of 800 citizens interviewed, 608 found it unacceptable. Find the point estimate of the population proportion of citizens of the country who find it unacceptable for a foreign government to monitor communications from their country's leaders. (Round to two decimal places as needed.)

.76

In the United States, the mean birth weight for boys is 3.41 kg, with a standard deviation of 0.55 kg. Assume that the distribution of birth weight is approximately normal. Typically, birth weight is between 2.5 kg and 4.0 kg. Find the probability a baby is born with typical birth weight. (Round to three decimal places as needed.)

.808

When 1,140 subjects were asked, "Do you believe in heaven?," 928 replied with yes. Find a point estimate of the proportion of people who believe in heaven. (Round to two decimal places as needed

.81

The Mental Development Index (MDI) of the Bayley Scales of Infant Development is a standardized measure used in observing infants over time. It is approximately normal with a mean of 100 and a standard deviation of 16. What proportion of children has an MDI of at least 78? (Round to four decimal places as needed.)

.9162

You'd like to estimate the proportion of the 13,500 undergraduate students at a university who are full-time students. You poll a random sample of 350 students, of whom 322 are full-time. Unknown to you, the proportion of all undergraduate students who are full-time students is 0.928. Let X denote a random variable for which x = 0 denotes part-time students and x = 1 denotes full-time students. The data distribution has P(1)=______. (Fill in the blank. Do not round. )

.92

Which z-score is used in a 99%, confidence interval for a population proportion?

2.575

Which z-score is used in a 90%, confidence interval for a population proportion?

1.645

Which z-score is used in a 95%, confidence interval for a population proportion?

1.96

Scores on a certain test are normally distributed with a variance of 14. A researcher wishes to estimate the mean score achieved by all adults on the test. Find the sample size needed to assure with 90% confidence that the sample mean will not differ from the population mean by more than 2 units.

10

The Mental Development Index (MDI) of the Bayley Scales of Infant Development is a standardized measure used in observing infants over time. It is approximately normal with a mean of 100 and a standard deviation of 16. Find the MDI score that is the 73rd percentile. (Round to two decimal places as needed.)

109.92

You plan to purchase dental insurance for your three remaining years in school. The insurance makes a one-time payment of $1500 in case of a major dental repair (such as an implant) or a one-time payment of $100 in case of a minor repair (such as a cavity). If you don't need dental repair over the next 3 years, the insurance expires and you receive no payout. You estimate the chances of requiring a major repair over the next 3 years as 4%, a minor repair as 59% and no repair as 37%. Let X = payout of dental insurance. How much should the insurance company expect to pay for this policy? (Hint: Find the mean for this probability distribution.) (Type an integer or a decimal. Do not round.)

119

According to a recent survey, the population distribution of number of years of education for self-employed individuals in a certain region has a mean of 13.4 and a standard deviation of 3.6. Find the mean of the sampling distribution of \bar x for a random sample of size 81. (Do not round.)

13.4

Suppose your favorite coffee machine offers 6 ounce cups of coffee. The actual amount of coffee put in the cup by the machine varies according to a normal distribution, with mean equal to 7 ounces and standard deviation equal to 0.62 ounces. Approximately what percentage of cups will be filled with between 7.62 and 8.24 ounces of coffee? (Type an integer or a decimal. Do not round.)

13.59

A World Health Organization study of health in various countries reported that in Canada, systolic blood pressure readings have a mean of 121 and a standard deviation of 16. A reading above 140 is considered to be high blood pressure. Find the 89th percentile of blood pressure readings. (Round to the nearest whole number as needed.)

141

Suppose your favorite coffee machine offers 6 ounce cups of coffee. The actual amount of coffee put in the cup by the machine varies according to a normal distribution, with mean equal to 7 ounces and standard deviation equal to 0.62 ounces. Approximately what percentage of cups will be filled with less than 6.38 ounces? (Type an integer or a decimal. Do not round.)

15.87

Suppose your favorite coffee machine offers 6 ounce cups of coffee. The actual amount of coffee put in the cup by the machine varies according to a normal distribution, with mean equal to 7 ounces and standard deviation equal to 0.62 ounces. Approximately what percentage of cups will be filled with more than 8.24 ounces? (Type an integer or a decimal. Do not round.)

2.28

Assume that the distribution of the score on a recent midterm is bell shaped with population mean \mu= 66 and population standard deviation \sigma = 8. You randomly sample n = 11 students who took the midterm. What is the standard deviation of the sampling distribution of the sample mean? (Round to two decimal places as needed.)

2.41

An exit poll is taken of 3,350 voters in a statewide election. Let X denote the number who voted in favor of a special proposition designed to lower property taxes and raise the sales tax. Suppose that in the population, exactly 60% voted for it. Find the mean of the probability distribution of X.

2010

An exit poll is taken of 3,350 voters in a statewide election. Let X denote the number who voted in favor of a special proposition designed to lower property taxes and raise the sales tax. Suppose that in the population, exactly 60% voted for it. Find the standard deviation of the probability distribution of X. (Round to three decimal places as needed.)

28.355

In the United States, the mean birth weight for boys is 3.41 kg, with a standard deviation of 0.55 kg. Assume that the distribution of birth weight is approximately normal. Max's parents are told that their newborn son falls at the 79th percentile. How much does Max weigh? (Round to two decimal places as needed.)

3.86

An exit poll is taken of 3,350 voters in a statewide election. Let X denote the number who voted in favor of a special proposition designed to lower property taxes and raise the sales tax. Suppose that in the population, exactly 60 % voted for it. Identify n for the binomial.

3350

Suppose your favorite coffee machine offers 6 ounce cups of coffee. The actual amount of coffee put in the cup by the machine varies according to a normal distribution, with mean equal to 7 ounces and standard deviation equal to 0.62 ounces. Approximately what percentage of cups will be filled with between 7 and 7.62 ounces of coffee? (Type an integer or a decimal. Do not round.)

34.13

Assume each newborn baby has a probability of approximately 0.49 of being female and 0.51 of being male. For a family with four children, let X = number of children who are girls. Identify n for the binomial distribution.

4

Suppose your favorite coffee machine offers 6 ounce cups of coffee. The actual amount of coffee put in the cup by the machine varies according to a normal distribution, with mean equal to 7 ounces and standard deviation equal to 0.62 ounces. What percentage of cups will be filled with less than 6 ounces? (Round to two decimal places as needed.)

5.37

In the United States, the mean birth weight for boys is 3.41 kg, with a standard deviation of 0.55 kg. Assume that the distribution of birth weight is approximately normal. Matteo weighs 3.5 kg at birth. He falls at what percentile? (Round to one decimal place as needed.)

56.4

On September 7, 2008, the Pittsburgh Pirates lost their 82nd game of the 2008 season and tied the 1933-1948 Philadelphia Phillies major sport record (baseball, football, basketball, and hockey) for most consecutive losing seasons at 16. In fact, their losing streak continued until 2012 with 20 consecutive losing seasons. A Major League Baseball season consists of 162 games, so for the Pirates to end their streak, they need to win at least 81 games in a season (which they did in 2013). Over the course of the streak, the Pirates have won approximately 42% of their games. For simplicity, assume the number of games they win in a given season follows a binomial distribution with n = 162 and p = 0.42. What is their expected number of wins in a season? (Round to two decimal places as needed.)

68.04

Suppose your favorite coffee machine offers 6 ounce cups of coffee. The actual amount of coffee put in the cup by the machine varies according to a normal distribution, with mean equal to 7 ounces and standard deviation equal to 0.62 ounces. Approximately what percentage of cups will have between 6.38 and 7.62 ounces of coffee? (Type an integer or a decimal. Do not round.)

68.26

From past experience, a wheat farmer finds that his annual profit (in dollars) is $87,000 if the summer weather is typical, $49,000 if the weather is unusually dry, and $25,000 if there is a severe storm that destroys much of his crop. Weather bureau records indicate that the probability is 0.65 of typical weather, 0.24 of unusually dry weather, and 0.11 of a severe storm. Let X denote the farmer's profit next year. Find the mean of the probability distribution of X. (Round to the narest dollar as needed.)

71,060

Suppose your favorite coffee machine offers 6 ounce cups of coffee. The actual amount of coffee put in the cup by the machine varies according to a normal distribution, with mean equal to 7 ounces and standard deviation equal to 0.62 ounces. What percentage of cups will be filled with more than 6.4 ounces? (Round to two decimal places as needed.)

83.15

A population is normal with a variance of 36. Suppose you wish to estimate the population mean \mu. Find the sample size needed to assure with 95% confidence that the sample mean will not differ from the population mean by more than 4 units.

9

The Mental Development Index (MDI) of the Bayley Scales of Infant Development is a standardized measure used in observing infants over time. It is approximately normal with a mean of 100 and a standard deviation of 16. Find the MDI score such that only 27% of the population has an index below it. (Round to two decimal places as needed.

90.24

Over roughly the past 100 years, the mean monthly April precipitation in Williamstown, Massachusetts, equaled 3.6 inches with a standard deviation of 1.6 inches. Assuming a normal distribution, an April precipitation of 7.5 inches corresponds to what percentile? (Round to one decimal place as needed.)

99.27

State the difference between a point estimate and an interval estimate. Choose the correct answer below.

A point estimate gives a single number, while an interval estimate gives a range of numbers

A random sample of 100 students is taken from a university with an enrollment of 10,000 students. Which part describes a bootstrap sample?

A sample of size 100 taken with replacement from the students in the sample

Explain why a point estimate alone is usually insufficient for statistical inference. Choose the correct answer below.

An interval estimate gives us a sense of the accuracy of the point estimate whereas a point estimate alone does not.

For a normal distribution, verify that the probability (rounded to two decimal places) within 0.61 standard deviations of the mean equals 0.46.

By a standard normal distribution table, the cumulative probability to the left of 0.61 is 0.7291. The cumulative probability to the left of -0.61 is 0.2709. 0.7291 - 0.2709 = 0.4582, which rounds to 0.46.

For a normal distribution, how would you show that a total probability of 0.21 falls more than z = 1.25 standard deviations from the mean?

Divide the probability 0.21 by two to find the amount in each tail, 0.105. Then subtract this from 1.0 to determine the cumulative probability associated with this z-score, 0.895. Look up this probability on a standard normal probability table to find the z-score of 1.25.

A company that is selling condos in Florida plans to send out an advertisement for the condos to 400 potential customers, in which they promise a free weekend at a resort on the Florida coast in exchange for agreeing to attend a four-hour sales presentation. The company would like to know how many people will accept this invitation. Its best guess is that 20% of customers will accept the offer. The company wants to use simulations to find the likely range for the proportion of the 400 customers who are actually going to accept the offer under this assumption. If you were to perform one simulation for a sample of size 400. Why do you not expect to get exactly 0.20 for the proportion?

Due to random variability, it is unlikely that exactly 20% of the customers in the sample will accept the offer.

Explain what the "95% confidence" refers to by describing the long-run interpretation. Choose the correct answer below.

If the same method is used to estimate the same population proportion many times, then about 95% of the intervals would contain the population proportion.

A study took a sample to investigate how video on demand and other subscription-based services change TV viewing behavior of adults in a certain country. Among others, the study recorded how many subscribers primarily watch content time-shifted (not live) and the weekly number of hours adults spend watching content over the Internet. The sample mean number of hours watched online is an unbiased estimator for what parameter? Explain what unbiased means.

It is an unbiased estimator for the mean weekly time adults in the country spend watching content over the Internet. An unbiased estimator is centered at the parameter it tries to estimate.

For a normal distribution, verify that the probability (rounded to two decimal places) within 2.24 standard deviations of the mean equals 0.98.

Looking up 2.24 in a standard normal distribution table, the cumulative probability is 0.9875. Likewise, the cumulative probability is 0.0125 for - 2.24. 0.9875 - 0.0125 = 0.9750, which rounds to 0.98.

A social scientist uses a survey to study how much time per day people spend commuting to work. The variable given on the survey website measures this using the values 0, 1, 2, ..., 24. Explain how, in theory, commuting is a continuous random variable

Someone could commute for exactly 1 hour or for 1.8643 hours.

A social scientist uses a survey to study how much time per day people spend commuting to work. The variable given on the survey website measures this using the values 0, 1, 2, ..., 24. Explain how, in theory, commuting is a continuous random variable.

Someone could commute for exactly 1 hour or for 1.8643 hours.

What assumptions are needed to construct a 95% confidence interval for the population mean \mu?

The data are obtained by randomization, and the population distribution is approximately normal.

When the COVID-19 pandemic broke out in March 2020, one of the important parameters for planning how to respond to the crisis was the proportion of a country's population that was infected with the virus. Because testing for the virus was only available for those who presented with severe symptoms (tests were in short supply), the proportion of those that tested positive for the virus was not a reliable estimate for the general population because many people that contracted the virus never showed any symptoms. In an effort to estimate this proportion, one country obtained what could be treated as a representative sample. During one week in March 2020, a genetics lab in this country tested 5,507 people, of which only 48 tested positive. Suppose a 95% confidence interval for the population proportion of infected people in this country around the time the testing took place is constructed. State the assumptions needed for this interval to be valid. Choose the correct answer below.

The data must be obtained randomly, and the expected numbers of successes and failures must both be at least 15.

The accompanying data include per capita energy consumption (in BTU) for a sample of 35 countries in the Organization for Economic Co-operation and Development (OECD) in 2011. Iceland had the highest per capita consumption, with 665 million BTU. How does this outlier (which is also an outlier in the population of all OECD countries) affect the sampling distribution of the mean? The true population distribution may be rather skewed, in which case a sample of size 35 might not be large enough for the Central Limit Theorem to apply. In such cases, the sampling distribution can be approximated via the bootstrap. Use the provided bootstrap sampling distribution output from 10,000 generated bootstrap samples to describe the bootstrap distribution of the sample mean.

The distribution is approximately bell shaped

A person's blood pressure is monitored by taking 4 readings daily. The probability distribution of his readings had a mean of 129 and a standard deviation of 8. Each set of daily observations behaves as a random sample. Suppose the probability distribution of the blood pressure readings is normal. Choose the correct description of the shape of the sampling distribution of \bar x for a sample size of 4.

The distribution is approximately normal.

Suppose that you want to construct a 95% confidence interval for estimating a population mean. How does the margin of error with a sample size of 100 compare with the margin of error with a sample size of 1,600, if both samples have the same standard deviation?

The margin of error for the first interval will be 16 times larger than the margin of error for the second interval.

In a certain year, according to a national Census Bureau, the number of people in a household had a mean of 4.39 and a standard deviation of 2.23. This is based on census information for the population. Suppose the Census Bureau instead had estimated this mean using a random sample of 375 homes. Suppose the sample had a sample mean of 4.2 and standard deviation of 2.1. Identify the random variable X.

The number of households in the country

A study dealing with health care issues plans to take a sample survey of 1500 Americans to estimate the proportion who have health insurance and the mean dollar amount that Americans spent on health care this past year. Identify two population parameters that this study will estimate. Chose the correct answers below. Select all that apply.

The population proportion who have health insurance The population mean dollar amount spent on health care this past year

The figure illustrates two sampling distributions for sample proportions when the population proportion p=.60. Explain why the sample proportion would be very likely to fall (i) between 0.48 and 0.72 when n = 150, and (ii) between 0.56 and 0.64 when n = 1500.

The sample proportion is very likely to fall within three standard deviations of the mean.

Access the Sampling Distribution of the Sample Mean app, select skewed population distribution, and change the option for the skewness to "extremely left". Simulate the sampling distribution when the sample size n = 2. Run 10,000 simulations and look at the resulting histogram of the sample means. What shape does the simulated sampling distribution have?

The sampling distribution is skewed left.

The table shows the probability distribution of the number of bases for a randomly selected time at bat for a random player on a certain baseball team. Verify that the probabilities give a legitimate probability distribution. Choose the correct answer below.

The sum of the probabilities is 1 and each probability falls between 0 and 1.

The juror pool for an upcoming trial contains 100,000 individuals in the population who may be called for jury duty. The proportion of the available jurors on the population list who are Hispanic is 0.44. A jury of size 8 is selected at random from the population list of available jurors. Let X = the number of Hispanics selected to be jurors for this jury. Explain why this scenario would seem to satisfy the three conditions needed to use the binomial distribution.

They are satisfied because 1) the data are binary (Hispanic or not), 2) the probability of success is always 0.44 and 3) the trials are independent (the first selection does not affect the next; n < 10% of population size).

An exit poll is taken of 3,350 voters in a statewide election. Let X denote the number who voted in favor of a special proposition designed to lower property taxes and raise the sales tax. Suppose that in the population, exactly 60 % voted for it. Explain why this scenario would seem to satisfy the three conditions needed to use the binomial distribution.

They are satisfied because 1) the data are binary (voted for recall or not), 2) there is the same probability of success for each trial (0.6), and 3) the trials are independent (one voter does not affect the next; n < 10% of population size).

When the COVID-19 pandemic broke out in March 2020, one of the important parameters for planning how to respond to the crisis was the proportion of a country's population that was infected with the virus. Because testing for the virus was only available for those who presented with severe symptoms (tests were in short supply), the proportion of those that tested positive for the virus was not a reliable estimate for the general population because many people that contracted the virus never showed any symptoms. In an effort to estimate this proportion, one country obtained what could be treated as a representative sample. During one week in March 2020, a genetics lab in this country tested 5,507 people, of which only 48 tested positive. Suppose a 95% confidence interval for the population proportion of infected people in this country around the time the testing took place is constructed. Interpret the confidence interval. Choose the correct answer below.

With 95% confidence, the limits of the confidence interval contain the proportion of people who tested positive forCOVID-19.

An organization's survey of one country's citizens asked whether they find it acceptable for a foreign government to monitor communications from their country's leaders. Results from the survey show that of 800 citizens interviewed, 608 found it unacceptable. The organization that conducted the survey reports a margin of error at the 95% confidence level of 3.0% for this survey. Explain what this means.

With a probability of 95%, the point estimate falls within a distance of 0.030 of the actual proportion of citizens of the country who find it unacceptable

You plan to purchase dental insurance for your three remaining years in school. The insurance makes a one-time payment of $1500 in case of a major dental repair (such as an implant) or a one-time payment of $100 in case of a minor repair (such as a cavity). If you don't need dental repair over the next 3 years, the insurance expires and you receive no payout. You estimate the chances of requiring a major repair over the next 3 years as 4%, a minor repair as 59% and no repair as 37%. Let X = payout of dental insurance. Is X discrete or continuous?

X is a discrete variable because the possible outcomes are a set of separate numbers.