Statistics Final Exam Review MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

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1 Statistics Final Exam Review Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Assume that X has a normal distribution, and find the indicated probability. 1) The mean is μ = 60.0 and the standard deviation is σ = 4.0. Find the probability that X is less than A) B) C) D) ) 2) The mean is μ = 15.2 and the standard deviation is σ = 0.9. Find the probability that X is greater than A) B) C) D) ) 3) The mean is μ = 15.2 and the standard deviation is σ = 0.9. Find the probability that X is between 14.3 and A) B) C) D) ) 4) The amount of rainfall in January in a certain city is normally distributed with a mean of 4.6 inches and a standard deviation of 0.3 inches. Find the value of the quartile Q1. A) 4.8 B) 4.5 C)4.4 D) 1.2 4) Find the indicated probability. 5) The weekly salaries of 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 teacher earns more than $525 a week? A) B) C) D) ) 6) The amount of snowfall falling in a certain mountain range is normally distributed with a mean of 74 inches, and a standard deviation of 12 inches. What is the probability that the mean annual snowfall during 36 randomly picked years will exceed 76.8 inches? A) B) C) D) ) 7) The weights of the fish in a certain lake are normally distributed with a mean of 12 lb and a standard deviation of 12. If 16 fish are randomly selected, what is the probability that the mean weight will be between 9.6 and 15.6 lb? A) B) C) D) ) Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution. 8) A certain question on a test is answered correctly by 22% of the respondents. Estimate the 8) probability that among the next 150 responses there will be at most 40 correct answers. A) B) C) D)

2 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Construct a normal probability plot of the given data. Use your plot to determine whether the data come from a normally distributed population. 9) The systolic blood pressure (in mmhg) is given below for a sample of 12 men aged 9) between 60 and y x MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 10) Find the critical value zα/2 that corresponds to a degree of confidence of 98%. A) B) 2.05 C) 2.33 D) ) Find the margin of error for the 95% confidence interval used to estimate the population proportion. 11) n = 169, x = 107 A) B) C) D) ) 12) In a survey of 4100 T.V. viewers, 20% said they watch network news programs. A) B) C) D) ) Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p. 13) n = 58, x = 28; 95 percent 13) A) < p < B) < p < C)0.374 < p < D) < p < Find the minimum sample size you should use to assure that your estimate of p^will be within the required margin of error around the population p. 14) Margin of error: 0.002; confidence level: 93%; p^ and q^ unknown A) 204,756 B) 204,757 C) 410 D) ) 15) Margin of error: 0.01; confidence level: 95%; from a prior study, p^ is estimated by the decimal equivalent of 69%. A) 26,507 B) 8218 C) 14,184 D) ) 2

3 Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p. 16) When 306 college students are randomly selected and surveyed, it is found that 115 own a car. Find 16) a 99% confidence interval for the true proportion of all college students who own a car. A) < p < B) < p < C)0.305 < p < D) < p < ) Of 129 randomly selected adults, 32 were found to have high blood pressure. Construct a 95% confidence interval for the true percentage of all adults that have high blood pressure. A) 15.9% < p < 33.7% B) 15.0% < p < 34.6% C)17.4% < p < 32.3% D) 18.5% < p < 31.1% 17) 18) A newspaper article about the results of a poll states: "In theory, the results of such a poll, in 99 cases out of 100 should differ by no more than 6 percentage points in either direction from what would have been obtained by interviewing all voters in the United States." Find the sample size suggested by this statement. A) 461 B) 19 C)268 D) ) Determine whether the given conditions justify using the margin of error E = z α/2 σ/ n when finding a confidence interval estimate of the population mean μ. 19) The sample size is n = 286 and σ = ) A) No B) Yes Use the confidence level and sample data to find the margin of error E. 20) Weights of eggs: 95% confidence; n = 47, x = 1.44 oz, σ = 0.39 oz A) 6.86 oz B) 0.09 oz C)0.11 oz D) 0.02 oz 20) Use the confidence level and sample data to find a confidence interval for estimating the population μ. 21) Test scores: n = 109, x = 79.1, σ = 6.9; 99 percent A) 77.8 < μ < 80.4 B) 77.4 < μ < 80.8 C)78.0 < μ < 80.2 D) 77.6 < μ < ) A laboratory tested 90 chicken eggs and found that the mean amount of cholesterol was 230 milligrams with σ = 16.0 milligrams. Construct a 95 percent confidence interval for the true mean cholesterol content, μ, of all such eggs. A) 227 < μ < 233 B) 226 < μ < 233 C)228 < μ < 234 D) 226 < μ < ) 22) Use the margin of error, confidence level, and standard deviation σ to find the minimum sample size required to estimate an unknown population mean μ. 23) Margin of error: $121, confidence level: 95%, σ = $528 23) A) 64 B) 4 C)2 D) 74 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. 24) 99%; n = 17; σ is unknown; population appears to be normally distributed. A) zα/2 = B) tα/2 = C)zα/2 = D) tα/2 = ) 25) 98%; n = 7; σ = 27; population appears to be normally distributed. A) zα/2 = 2.33 B) tα/2 = C)zα/2 = 2.05 D) tα/2 = ) 3

4 Find the margin of error. _ 26) 95% confidence interval; n = 91 ; x = 72, s = 11.4 A) 4.57 B) 2.03 C) 2.13 D) ) Use the given degree of confidence and sample data to construct a confidence interval for the population mean μ. Assume that the population has a normal distribution. 27) n = 30, x = 86.5, s = 10.3, 90 percent A) < μ < B) < μ < C)83.31 < μ < D) < μ < ) 28) A laboratory tested twelve chicken eggs and found that the mean amount of cholesterol was 193 milligrams with s = 15.4 milligrams. Construct a 95 percent confidence interval for the true mean cholesterol content of all such eggs. A) < μ < B) < μ < C)183.3 < μ < D) < μ < ) 29) Find the critical value χ 2 R corresponding to a sample size of 11 and a confidence level of 90 29) percent. A) 3.94 B) C) D) Use the given degree of confidence and sample data to find a confidence interval for the population standard deviation σ. Assume that the population has a normal distribution. 30) Weights of men: 90% confidence; n = 14, x = lb, s = 12.6 lb A) 9.9 lb < σ < 16.3 lb B) 9.6 lb < σ < 18.7 lb C)10.2 lb < σ < 2.7 lb D) 9.3 lb < σ < 17.7 lb 30) Find the appropriate minimum sample size. 31) You want to be 99% confident that the sample standard deviation s is within 5% of the population standard deviation. A) 2,638 B) 2,434 C) 923 D) 1,335 31) Use the given degree of confidence and sample data to find a confidence interval for the population standard deviation σ. Assume that the population has a normal distribution. 32) The daily intakes of milk (in ounces) for ten randomly selected people were: 32) Find a 99 percent confidence interval for the population standard deviation σ. A) (3.38, 11.20) B) (0.83, 3.28) C)(3.27, 11.20) D) (3.38, 12.46) Express the null hypothesis H0 and the alternative hypothesis H1in symbolic form. Use the correct symbol (μ, p, σ )for the indicated parameter. 33) A skeptical paranormal researcher claims that the proportion of Americans that have seen a UFO, p, is less than 2 in every one thousand. A) H0: p < B) H0: p = C)H0: p = D) H0: p > H1: p H1: p > H1: p < H1: p ) 4

5 34) Carter Motor Company claims that its new sedan, the Libra, will average better than 30 miles per gallon in the city. Use μ, the true average mileage of the Libra. A) H0: μ = 30 H1: μ < 30 B) H0: μ < 30 H1: μ 30 C)H0: μ = 30 H1: μ > 30 D) H0: μ > 30 H1: μ 30 34) 35) A researcher claims that 62% of voters favor gun control. A) H0: p = 0.62 H1: p 0.62 B) H0: p 0.62 H1: p < 0.62 C)H0: p 0.62 H1: p = 0.62 D) H0: p < 0.62 H1: p ) Use the given information to find the P-value. 36) The test statistic in a left-tailed test is z = A) B) C) D) ) 37) The test statistic in a two-tailed test is z = A) B) C) D) ) Formulate the indicated conclusion in nontechnical terms. Be sure to address the original claim. 38) A cereal company claims that the mean weight of the cereal in its packets is at least 14 oz. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms. A) There is not sufficient evidence to warrant rejection of the claim that the mean weight is at least 14 oz. B) There is not sufficient evidence to warrant rejection of the claim that the mean weight is less than 14 oz. C)There is sufficient evidence to warrant rejection of the claim that the mean weight is less than 14 oz. D) There is sufficient evidence to warrant rejection of the claim that the mean weight is at least 14 oz. 38) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. 39) Various temperature measurements are recorded at different times for a particular city. 39) The mean of 20 C is obtained for 40 temperatures on 40 different days. Assuming that σ = 1.5 C, test the claim that the population mean is 23 C. Use a 0.05 significance level. Test the given claim using the traditional method of hypothesis testing. Assume that the sample has been randomly selected from a population with a normal distribution. 40) In tests of a computer component, it is found that the mean time between failures is ) hours. A modification is made which is supposed to increase the time between failures. Tests on a random sample of 10 modified components resulted in the following times (in hours) between failures At the 0.05 significance level, test the claim that for the modified components, the mean time between failures is greater than 520 hours. 5

6 Use the traditional method to test the given hypothesis. Assume that the population is normally distributed and that the sample has been randomly selected. 41) The standard deviation of math test scores at one high school is A teacher claims that 41) the standard deviation of the girls' test scores is smaller than A random sample of 22 girls results in scores with a standard deviation of Use a significance level of 0.01 to test the teacher's claim. 42) a) An Accountemps survey of 150 executives showed that 44% of them say that little or no knowledge of the company is the most common mistake made by candidates during job interviews. Use a 0.05 significance level to test the claim that less than half of all executives identify that error as being the most common job interviewing error. 42) b) Glamour magazine sponsored a survey of 2500 prospective brides and found that 60% of them spent less than $750 on their wedding gown. Use a 0.01 significance level to test the claim that less than 62% of brides spend less than $750 on their wedding gown. c) A student of the author randomly selected 70 packets of sugar and weighed the contents of each packet, getting a mean of grams and a standard deviation of grams. Test the claim that the weights of the sugar packets have a mean equal to 3.5 grams, as indicated on the label. d) The Orange County Bureau of Weights and Measures received complaints that the Windsor Bottling Company was cheating consumers by putting less than 12 ounces of root beer in its cans. When 24 cans are randomly selected and measured, the amounts are found to have a mean of 11.4 ounces and a standard deviation of 0.62 ounces. Use the sample data to test the claim that consumers are being cheated. e) In clinical tests of the drug Lipitor, 863 patients experience flu symptoms. Use a 0.01 significance level to test the claim that the percentage of treated patients with flu symptoms is greater than the 1.9% rate for patients not given the treatment. f) For a simple random sample of adults, IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. A simple random sample of 13 statistics professors yields a standard deviation of s=7.2. A psychologist is quite sure that statistics professors have IQ scores that have a mean greater than 100. He claims that statistics professors have IQ scores with a standard deviation equal to 15, the same standard deviation for the general population. Assume that IQ scores of statistics professors are normally distributed and use a 0.05 significance level to test the claim that σ = 15. g) A calculator randomly generates 50 numbers with μ = 100 and σ = 15. One such generated sample of 50 values has a mean of 98.4 and a standard deviation of Use a.10 significance level to test the claim that the sample actually does come from a population with a mean equal to 100. h) A premed student plans to collect her sample to test the claim that the mean body temperature is less than 98.6 degrees, as is commonly believed. She collects data froom 12 people. She measures their body temperatures and obtains 12 scores not listed below. Use a 0.05 significance level to test the 6

7 claim that these body temperatures come from a population with a mean that is less than 98.6 degrees. i) Women have heights with a mean of 64.1 inches and a standard deviation of 2.52 inches. The sample of 40 heights have a mean of inches and a standard deviation of 2.74 inches. Use a 0.05 significance level to test the claim that this sample is from a population with a standard deviation equal to 2.52 inches. 7

8 Answer Key Testname: STATISTICS FINAL EXAM REVIEW 1) C 2) C 3) B 4) C 5) A 6) A 7) C 8) D 9) Because the points lie roughly on a straight line, it appears that the data come from a normally distributed population. 10) C 11) B 12) A 13) D 14) B 15) B 16) C 17) C 18) A 19) B 20) C 21) B 22) A 23) D 24) B 25) A 26) D 27) C 28) B 29) B 30) B 31) D 32) D 33) C 34) C 8

9 Answer Key Testname: STATISTICS FINAL EXAM REVIEW 35) A 36) B 37) B 38) D 39) H0: μ = 23; H1: μ > 23. Test statistic: z = ;. P-value: Because the P-value of is less than the significance level of α = 0.05,we reject the null hypothesis. 40) Test statistic: t = Critical value: t = Reject H0. There is sufficient evidence to support the claim that the mean is greater than 520 hours. 41) Test statistic: X2 = Critical value: X2 = Fail to reject H0. There is not sufficient evidence to support the claim that the standard deviation of the girls' test scores is smaller than ) 9