Stats Practice Problems #1

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Using the table from problem #7 above, find P(Moderate │ Republican). A) 535746 B) 146746 C) 146535 D) 1461904

C) 146535

Find the mean of the following probability distribution. X P(X) 0 0.055, 1 0.326, 2 0.583, 3 0.036 A) 1.6 B) 1 C) 0.17 D) 0.25

A) 1.6

Roll a fair six-sided die. You win $7 if you roll a number greater than 3. You will lose $3 if you roll the number 2. If you roll any other number, you will neither win nor lose anything. Find the expected value (winnings) of this probability experiment to the nearest cent. A) $3.00 B) $5.00 C) $2.00 D) $4.17

A) $3.00

What are the two requirements of any discrete probability distribution? A) 0 _< P(X)_< 1 and EP(X)=1 B) -1 < P(X) < 1 and EP(X)=1 C) -1_< P(X)_< 1 and EP(X)=1 D) 0 < P(X) < 1 and E X=1

A) 0 _< P(X)_< 1 and EP(X)=1

Use the following information to answer the question. Suppose that a recent poll of American households about pet ownership found that for households with one pet, 39% owned a dog, 33% owned a cat, and 7% owned a bird. Suppose that three households are selected randomly and with replacement. What is the probability that none of the three randomly selected households own a cat? (Round to the nearest hundredth) A) 0.30 B) 0.46 C) 0.67 D) 0.70

A) 0.30

Use the following information to answer the question. The mean age of lead actors from the top ten grossing movies of 2007 was 36.4 years with a standard deviation of 9.87 years. Assume the distribution of the actors ages is approximately unimodal and symmetric. Between what two values would you expect to find about 68% of the lead actors ages? A) 26.53 and 46.27 years B) 6.87 and 66.01 years C) 16.66 and 56.14 years D) None of these

A) 26.53 and 46.27 years

A university dean is interested in determining the proportion of students who receive some sort offinancial aid. Rather than examine the records for all students, the dean randomly selects 200students and finds that 118 of them are receiving financial aid. The 95% confidence interval for thepercentage of students who receive financial aid is (52.2%, 65.8%). Suppose that in the past, 53% ofstudents received financial aid. Does the confidence interval support or refute the claim that thepercentage of students receiving financial aid has increased? A) The interval does not support this claim. This is because 53% is in the interval. B) The interval supports this claim. This is because 53% is not in the interval, and most of the values are above 53%. C) The interval supports this claim. This is because 53% is in the interval. D) The interval does not support this claim. This is because 53% is not in the interval, and most of the values are above 53%.

A) The interval does not support this claim. This is because 53% is in the interval.

Use the following information to answer the question. A sprint duathlon consists of a 5 km run, a 20 km bike ride, followed by another 5 km run. The mean finish time of all participants in a recent large duathlon was 1.67 hours with a standard deviation of 0.25 hours. Suppose a random sample of 30 participants was taken and the mean finishing time was found to be1.59 hours with a standard deviation of 0.30 hours. What is the standard error for the mean finish time of 30 randomly selected participants? Round to the nearest thousandth. A) 0.300 B) 0.046 C) 0.055 D) 0.250

B) 0.046

According to a recent study, 25% of all U.S. households are wireless-only households (no landline). In a random sample of 20 households, what is the probability that 3 or fewer households are wireless-only?(nearest thousandth) A) 0.150 B) 0.225 C) 0.999 D) 0.134

B) 0.225

The weights at birth of five randomly chosen baby giraffes were 111, 115, 120, 103, and 106 pounds. Assume the distribution of weights is normally distributed. Find a 95% confidence interval for the mean weight of all baby giraffes. Use technology for your calculations. Give the confidence interval in the form "estimate ± margin of error." Round to the nearest tenth of a pound. A) 111.5 ± 9.0 pounds B) 111.0 ± 8.5 pounds C) 110.0 ± 8.5 pounds D) There is not enough information given to calculate the confidence interval.

B) 111.0 ± 8.5 pounds

At the district spelling bee, the 60 girls have a mean score of 71 points with a standard deviation of 6, while the 50 boys have a mean score of 66 with a standard deviation of 5 points. Which score is more unusual: Mary's score of 80 or John's score of 75? A) They are the same. B) John's score is more unusual. C) Mary's score is more unusual. D) It cannot be determined which exam score is more unusual.

B) John's score is more unusual.

The table below summarizes results from a survey that asked about political affiliation and self-described political orientation. One person is randomly selected from the sample summarized below.We want to find the probability that a liberal person is a Democrat. Democrat Republican Other Total Liberal 311 49 169 529 Moderate 285 146 315 746 Conservative 120 340 169 629 Total 716 535 653 1904 Which of the following statements best describes the problem? A) P(Liberal │ Democrat) B) P(Democrat │ Liberal) C) P(Democrat AND Liberal) D) P(Democrat OR Liberal)

B) P(Democrat │ Liberal)

Use the following information for questions 15 - 16. A janitor at a large office building believes that his supply of light bulbs has a defect rate greater than the defect rate stated by the manufacturer. The janitor's null hypothesis is that the supply of light bulbs has a defect rate of p = 0.09 (the light bulb manufacturer's stated defect rate). Suppose we do a hypothesis test with a significance level of 0.01. Symbolically, the null and alternative hypothesis are as follows: H0: p = 0.09 andHa: p > 0.09. Suppose the janitor tests 300 light bulbs and finds that 33 bulbs are defective. What value of the test statistic should he report? Round to the nearest hundredth. A) z = -2.17 B) z = 1.21 C) z = 2.17 D) z = -1.21

B) z = 1.21

Historically, the percentage of residents of a certain country who support the death penalty has been 52%. A recent poll of 911 people showed 452 in favor of the death penalty. Assume the poll was given to a random sample of people. Suppose we want to test the claim that the proportion of those favoring the death penalty has changed. Find the standard error. Round to four decimal places as needed. A) 0.4962 B) 1.4401 C) 0.0166 D) 0.0003

C) 0.0166

Suppose that the average classical music piece in Europe is 4 minutes with a standard deviation of 1.25 minutes. It is known that song length is not normally distributed. Suppose a sample of 25 songs is taken from the population. What is the approximate probability that the average song length will be less than 3.5 minutes? Round to the nearest thousandth. A) 0.345 B) 0.477 C) 0.023 D) 0.155

C) 0.023

According to a candy company, packages of a certain candy contain 17% yellow candies. Suppose we examine 50 random candies. What is the standard error? (Show your work and round to three decimal places as needed.) A) 0.003 B) 0.008 C) 0.053 D) 0.421

C) 0.053

Assume that adults have IQ scores that are normally distributed with a mean, μ = 105, and a standarddeviation σ = 20. What is the probability that a randomly selected adult has an IQ score of less than 90?(Use either your graphing calculator or a Z-table.) Round your answer to the nearest hundredth. A) 0.50 B) 0.77 C) 0.23 D) 0.18

C) 0.23

Suppose the probability that a stolen car is recovered is 0.35. Consider a sample of twelve randomly selected people who recently had their car stolen. What is the probability that exactly four out of these twelve people had their car recovered? Round your answer to the nearest thousandth. A) 0.333 B) 0.583 C) 0.237 D) 0.020

C) 0.237

Which of the following is the correct decision and conclusion for this hypothesis test? Please show your work. A) Do not reject H0. There is enough evidence to support the claim that the proportion of those favoring gun control has changed. B) Reject H0. There is not enough evidence to support the claim that the proportion of those favoring gun control has changed. C) Do not reject H0. There is not enough evidence to support the claim that the proportion of those favoring gun control has changed. D) Reject H0. There is enough evidence to support the claim that the proportion of those favoring gun control has changed.

C) Do not reject H0. There is not enough evidence to support the claim that the proportion of those favoring gun control has changed.

In a simple random sample of 1200 Americans age 20 and over, the proportion with diabetes was found to be 0.115 (or 11.5%). Report the 95% confidence interval for the proportion of all Americans age 20 and over with diabetes. (Please show your work and round your standard error to 4 digits for calculations. Round your answer to one decimal place. A) (10.3%, 12.7%) B) (10.0%, 13.0%) C) (9.1%, 13.9%) D) (9.7%,13.3%)

D) (9.7%,13.3%)

According to the National Nursing Association, approximately 61% of people who take the board exam to become a licensed nurse pass the exam. Find the probability that at least 68% of 100 randomly sampled people taking the nursing board exam passed. Round your standard error to four digits for calculation and round your answer to four digits. Please show all your work. A) 0.9335 B) 0.0665 C) 0.2211 D) 0.0757

D) 0.0757

The quantitative scores on a test are approximately normally distributed with a mean of 250 and a standard deviation of 75. Using either your graphing calculator or a Z-table, find the probability that a given score on this test is between 240 and 310. Round your answer to the nearest hundredth. A) 0.45 B) 0.50 C) 0.21 D) 0.34

D) 0.34

Which of the following is not a true statement about the Central Limit Theorem for sample means? A) If conditions are met, the mean of the sampling distribution is equal to the population mean. B) If the sample size is large, it doesn't matter what the distribution of the population it was drawn from is, the normal distribution can still be used to perform statistical inference. C) The Central Limit Theorem helps us find probabilities for sample means when those meansare based on a random sample from a population. D) All of these statements are true about the Central Limit Theorem for sample means.

D) All of these statements are true about the Central Limit Theorem for sample means.

Which one of the following variables is NOT discrete? A) The number of people waiting at a bus stop. B) How many siblings a person has. C) The number of blouses a buyer purchased at the latest Kohl's sale. D) The amount of snowfall in Boston this winter.

D) The amount of snowfall in Boston this winter.

A manufacturer claims that the mean lifetime of its lithium batteries is 1400 hours. Ahomeowner selects 25 of these batteries and finds the mean lifetime to be 1380 hours with a standard deviation of 80 hours. Test the manufacturer's claim. Use α = 0.05. Round the test statistic to the nearest thousandth.

critical value t0 = ±2.064; standardized test statistic ≈ -1.25; fail to reject H0; There is not sufficient evidence to reject the manufacturer's claim.


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