stat test 3 biyogmum

1.61

Find the margin of error A survey found that 89% of a random sample of 1024 American adults approved of cloning endangered animals. Find the margin of error for this survey if we want 90% confidence in our estimate of the percentage of American adults who approve of cloning endangered animals.

2.9%

Find the mean and standard deviation of the sampling distribution of the proportion. A realtor has been told that 43% of homeowners in a city prefer to have a finished basement. She surveys a group of 300 homeowners randomly chosen from her client list. Describe the sampling distribution model of the proportion of homeowners in this sample who prefer a finished basement.

8%, 1.1%

Find the mean and standard deviation of the sampling distribution of the proportion. Based on past experience, a bank believes that 8% of the people who receive loans will not make payments on time. The bank has recently approved 600 loans. Describe the sampling distribution model of the proportion of clients in this group who may not make timely payments.

1.67

Find the mean of the binomial random variable. A die is rolled 10 times and the number of times that two shows on the up face is counted. If this experiment is repeated many times, find the mean for the random variable X, the number of twos thrown out of ten tosses.

3.52

Find the mean of the binomial random variable. According to a college survey, 22% of all students work full time. Find the mean for the random variable X, the number of students who work full time in samples of size 16.

3

Find the sample size A population is normal with a variance of 36. Suppose you wish to estimate the population mean μ. Find the sample size needed to assure with 68% confidence that the sample mean will not differ from the population mean by more than 4 units.

89

Find the sample size Weights of women in one age group are normally distributed with a standard deviation σ of 20 lb. A researcher wishes to estimate the mean weight of all women in this age group. Find how large a sample must be drawn in order to be 90% confident that the sample mean will not differ from the population mean by more than 3.5 lb.

.4930-.3932

Find the specified probability distribution of the binomial random variable. In one city, 21% of the population is under 25 years of age. Three people are selected at random from the city. Find the probability distribution of X, the number among the three that are under 25 years of age.

1.66

Find the standard deviation of the binomial random variable. According to a college survey, 22% of all students work full time. Find the standard deviation for the random variable X, the number of students who work full time in samples of size 16.

1.732

Find the standard deviation of the binomial random variable. On a multiple choice test with 16 questions, each question has four possible answers, one of which is correct. For students who guess at all answers, find the standard deviation for the random variable X, the number of correct answers.

.0367

Find the standard error A poll of 163 voters resulted in 110 favorable responses. Find the standard error for the sample proportion.

113.9, 4.0

For samples of the specified size from the population described, find the mean and standard deviation of the sampling distribution of the sample mean . The mean and the standard deviation of the sampled population are, respectively, 113.9 and 32.1. n = 64

Yes, -4.41

Is the observed sample proportion unusual? Based on previous studies, researchers believe that 6% of children are born with a gene that is linked to a certain childhood disease. If the researchers test 950 newborns for the presence of this gene, would it be unlikely for them to find fewer than 25 children with the gene? Answer by calculating the appropriate z-score. Round to the nearest hundredth when necessary.

3.20%

Provide an appropriate response. A 90% confidence interval for the mean percentage of airline reservations being canceled on the day of the flight is (1.3%, 5.1%). What is the point estimate of the mean percentage of reservations that are canceled on the day of the flight?

margin of error

Provide an appropriate response. A confidence interval for a parameter is constructed by adding and subtracting a ________ to a given point estimate.

both

Provide an appropriate response. A good estimator of a parameter has which of the following properties? I) the standard deviation of the estimator is small II) the estimator is unbiased III) the estimator has a high confidence level

2401

Provide an appropriate response. A pollster wishes to estimate the true proportion of U.S. voters who oppose capital punishment. How many voters should be surveyed in order to be 95% confident that the true proportion is estimated to within 2%?

.343

Find the indicated probability. A basketball player has made 70% of his foul shots during the season. If he shoots 3 foul shots in tonight's game, what is the probability that he makes all of the shots?

.2627

Find the indicated probability. An archer is able to hit the bull's-eye 55% of the time. If she shoots 8 arrows, what is the probability that she gets exactly 4 bull's-eyes? Assume each shot is independent of the others.

.178

Find the indicated probability. Police estimate that 25% of drivers drive without their seat belts. If they stop 6 drivers at random, find the probability that all of them are wearing their seat belts.

Are satisfied

Determine whether the conditions for the binomial distribution are satisfied. If the conditions are not satisfied, state why not. A polling agency in one city randomly selects 1000 registered voters from a pool of 385,600 registered voters of whom 17% are African American. X = number of African Americans in the sample.

Are not independent

Determine whether the conditions for the binomial distribution are satisfied. If the conditions are not satisfied, state why not. X = number of rainy days during the first 10 days of January in one city, given that it rains on 20% of days in January in that city.

.1971

Find the indicated probability for the normally distributed variable. In one region, the September energy consumption levels for single-family homes are normally distributed with a mean of 1050 kWh and a standard deviation of 218 kWh. For a randomly selected home, find the probability that the September energy consumption level is between 1100 kWh and 1225 kWh.

2.28%

Find the indicated probability for the normally distributed variable. The diameters of bolts produced by a certain machine are normally distributed with a mean of 0.30 inches and a standard deviation of 0.01 inches. What percentage of bolts will have a diameter greater than 0.32 inches?

.74

Find the indicated probability for the normally distributed variable. The percent of the voting-age population that is registered to vote for the 50 states and the District of Columbia has a mean of 65% with a standard deviation of 7.1. Assuming that the distribution is normal, what percentage of states had between 50 and 70 percent of it's voting-age population who are registered to vote?

.2177

Find the indicated probability for the normally distributed variable. The weekly salaries of elementary school teachers in one state are normally distributed with a mean of $490 and a standard deviation of $45. What is the probability that a randomly selected elementary school teacher earns more than $525 a week?

270

Provide an appropriate response. A university's administrator proposes to do an analysis of the proportion of graduates who have not found employment in their major field one year after graduation. In previous years, the percentage averaged 7%. He wants the margin of error to be within 4% at a 99% confidence level. What sample size will suffice? Use 2.575 as the critical value for a 99% confidence interval.

59,126

Provide an appropriate response. According to a recent survey, the mean income before taxes of consumer units (i.e., households) in the U.S. was $60,533 with a margin of error equal to 1406.32 (for a 95% confidence level). Calculate a 95% confidence level for the population mean income before taxes for all U.S. consumer units.

.9811

Provide an appropriate response. Assume that the heights of adult Caucasian women have a mean of 63.6 inches and a standard deviation of 2.5 inches. If 75 women are randomly selected, find the probability that they have a mean height between 63 and 65 inches.

wider, larger

Provide an appropriate response. In a survey of 1,000 television viewers, 40% said they watch network news programs. For a 90% confidence level, the margin of error for this estimate is 2.5%. If we want to be 92.5% confident, how will the margin of error change?

narrow, smaller

Provide an appropriate response. In a survey of 1,000 television viewers, 40% said they watch network news programs. For a 99% confidence level, the margin of error for this estimate is 3.99%. If we only want to be 90% confident, how will the margin of error change?

.043

Provide an appropriate response. In a survey of 500 residents, 300 were opposed to the use of the photo-cop for issuing traffic tickets. The standard error of the estimate is found to be 0.022. Find the margin of error that corresponds to a 95% confidence interval.

-2.2

Provide an appropriate response. In monitoring the levels of lead in the air after an explosion at a battery factory, it is found that the amounts of lead (in ug/m3) over a 6 day period had a mean of 1.54 and a standard error of 1.91. Construct a 95% confidence interval for the population mean.

30.83

Provide an appropriate response. In one region, the September energy consumption levels for single-family homes had a mean of 1050 kWh and a standard deviation of 218 kWh. Describe the center and variability of the sampling distribution of the sample mean for a random sample of 50 single-family homes from this region.

standard

Provide an appropriate response. In practice a _____ is an estimated standard deviation of a sampling distribution.

first, 5

Provide an appropriate response. 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 2500, if both samples have the same standard deviation?

margin of error

Provide an appropriate response. The _____ measures how accurate the point estimate is likely to be in estimating a parameter.

.2881

Provide an appropriate response. The gestation time for humans has a mean of 266 days and a standard deviation of 25 days. If 100 women are randomly selected, find the probability that they have a mean pregnancy between 266 days and 268 days.

both

Provide an appropriate response. The sample mean and the sample proportion are ______ of the population mean and the population proportion, respectively.

P(1)=.54

Select the most appropriate answer. A student group at a university conducted a poll to determine what percentage of students would vote republican in the upcoming presidential election. The poll randomly surveyed 500 students, 275 of which were female. If 54% of the university's 8200 students are female, which of the following identifies the population distribution of gender at this university?

60%

Select the most appropriate answer. In a survey of 500 residents, 300 were opposed to the use of the photo-cop for issuing traffic tickets. What is the best point estimate for the proportion of all residents opposed to the photo-cop use?

wider

Select the most appropriate answer. When a higher confidence level is used to estimate a proportion and all other factors involved are held constant

X is continuous

Select the most appropriate answer. Which of the following is not true about the binomial distribution?

120,152

Solve the problem. A speed-dating agency claims that 80% of the participants in its speed-dating evenings leave with at least one second date arranged. Suppose that 170 people participate in a speed-dating evening. Let X be the number who leave with at least one second date arranged. Assume that this scenario satisfies the conditions for the binomial distribution and use the normal distribution approximation to give an interval in which you would expect X almost certainly to fall, if it is true that

.6424

Solve the problem. For a normal distribution, find the probability that an observation falls within 0.92 standard deviations of the mean. Sketch a graph and shade the appropriate region.

-1.34

Use a table of areas for the standard normal curve to find the required z-score. Find the z-score having area 0.09 to its left under the standard normal curve.

.9656

Use a table of areas to find the specified area under the standard normal curve. The area that lies to the right of -1.82

12

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion. Of 346 items tested, 12 are found to be defective. Construct a 98% confidence interval to estimate the proportion of all such items that are defective.

1/16-1/4

When a coin is tossed four times, sixteen equally likely outcomes are possible as shown below: HHHH, HHHT, HHTH, HHTT HTHH, HTHT, HTTH, HTTT THHH, THHT, THTH, THTT TTHH, TTHT, TTTH, TTTT Let X denote the total number of tails obtained in the four tosses. Find the probability distribution of the random variable X. Leave your probabilities in fraction form.

.167-.056

When two balanced dice are rolled, 36 equally likely outcomes are possible as shown below. (1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6) (2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6) (3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6) (4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6) (5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6) (6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6) Let X denote the absolute value of the difference of the two numbers. Find the probability distribution of X. Give the probabilities as decimals rounded to three decimal places.