SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

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1 Math 1342 Final Exam Review SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Construct and interpret a boxplot or a modified boxplot as specified. 1) The weights (in pounds) of 30 newborn babies are listed below. Construct a boxplot for the data ) 2) The test scores of 40 students are listed below. Construct a boxplot for the data. 2) Find the indicated probability or percentage for the normally distributed variable. 3) The incomes of trainees at a local mill are normally distributed with a mean of $1,100 and a standard deviation $150. What percentage of trainees earn less than $900 a month? 3) 4) The volumes of soda in quart soda bottles are normally distributed with a mean of 32.3 oz and a standard deviation of 1.2 oz. What is the probability that the volume of soda in a randomly selected bottle will be less than 32 oz? 4) 5) A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. If an applicant is randomly selected, find the probability of a rating that is between 200 and ) 6) A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. If an applicant is randomly selected, find the probability of a rating that is between 170 and ) 7) The lengths of human pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. What is the probability that a pregnancy lasts at least 300 days? 7) 8) Assume that the weights of quarters are normally distributed with a mean of 5.67 g and a standard deviation g. A vending machine will only accept coins weighing between 5.48 g and 5.82 g. What percentage of legal quarters will be rejected? 8) 1

2 Find the confidence interval specified. 9) Physiologists often use the forced vital capacity as a way to assess a person's ability to move air in and out of their lungs. A researcher wishes to estimate the forced vital capacity of people suffering from asthma. A random sample of 15 asthmatics yields the following data on forced vital capacity, in liters. 9) Use the data to obtain a 95.44% confidence interval for the mean forced vital capacity for all asthmatics. Assume that σ = ) A random sample of 106 light bulbs had a mean life of x = 526 hours. Assume that σ = 29 hours. Construct a 90% confidence interval for the mean life, μ, of all light bulbs of this type. 10) 11) A random sample of 131 full-grown lobsters had a mean weight of 20 ounces. Assume that σ = 3.9 ounces. Construct a 95% confidence interval for the population mean μ. 11) Find the confidence interval specified. Assume that the population is normally distributed. 12) A laboratory tested twelve chicken eggs and found that the mean amount of cholesterol was 243 milligrams with s = 16.2 milligrams. Construct a 95% confidence interval for the true mean cholesterol content of all such eggs. 12) 13) Thirty randomly selected students took the calculus final. If the sample mean was 83 and the standard deviation was 14.1, construct a 99% confidence interval for the mean score of all students. 13) 14) A sociologist develops a test to measure attitudes about public transportation, and 27 randomly selected subjects are given the test. Their mean score is 76.2 and their standard deviation is Construct the 95% confidence interval for the mean score of all such subjects. 14) Provide an appropriate response. 15) A hypothesis test is performed at the 5% significance level to determine whether the mean body temperature for a certain population differs from 37.1 C. The hypotheses are H 0 : μ = 37.1 C H a : μ 37.1 C. Explain the difference between statistical significance and practical significance. 16) A right-tailed hypothesis test for a population mean is to be performed. If the null hypothesis is rejected at the 5% level of significance, does this necessarily mean that it would be rejected at the 1% level of significance? at the 10% level of signifiance? Explain your reasoning. In your explanation, refer to the critical values corresponding to the different significance levels. 15) 16) 2

3 17) In 1995, the mean math SAT score for students at one school was 488. A teacher introduces a new teaching method to prepare students for the SAT. One year later, he performs a hypothesis test to determine whether the mean math SAT score has increased. The hypotheses are H 0 : μ = 488 H a : μ > 488. If the null hypothesis is rejected at the 10% level of significance, do you think the teacher would feel confident that his teaching method works? What about if the null hypothesis is rejected at the 1% level of significance? Which of these two results would constitute stronger evidence that his teaching method works? Explain your thinking. 17) Preliminary data analyses indicate that it is reasonable to use a t-test to carry out the specified hypothesis test. Perform the t-test using the critical-value approach. 18) A test of sobriety involves measuring the subject's motor skills. The mean score for men 18) who are sober is known to be A researcher would like to perform a hypothesis test to determine whether the mean score for sober women differs from Twenty randomly selected sober women take the test and produce a mean score of 41.0 with a standard deviation of 3.7. Perform the hypothesis test at the 0.01 level of significance. 19) A large software company gives job applicants a test of programming ability and the mean for that test has been 160 in the past. Twenty-five job applicants are randomly selected from a large university and they produce a mean score of 183 and standard deviation of 12. Use a 0.05 level of significance to test whether the mean score for students from this university is greater than ) 20) In one state, the mean time served in prison by convicted burglars is 18.7 months. A researcher would like to perform a hypothesis test to determine whether the mean amount of time served by convicted burglars in her hometown is different from 18.7 months. She takes a random sample of 11 such cases from court files in her home town and finds that x = 20.7 months and s = 7.7 months. Use a significance level of 0.05 to perform the test. 20) Apply the pooled t-interval procedure to obtain the required confidence interval. You may assume that the assumptions for using the procedure are satisfied. 21) A researcher was interested in comparing the amount of time spent watching television by 21) women and by men. Independent simple random samples of 14 women and 17 men were selected and each person was asked how many hours he or she had watched television during the previous week. The summary statistics are as follows. Women Men x 1 = 11.4 x 2 = 17.4 s1 = 4.0 s2 = 4.1 n1 = 14 n2 = 17 Determine a 95% confidence interval for the difference between the mean weekly television watching times of women and men. 3

4 22) A paint manufacturer wanted to compare the drying times of two different types of paint. Independent simple random samples of 11 cans of type A and 9 cans of type B were selected and applied to similar surfaces. The drying times, in hours, were recorded. The summary statistics are as follows. 22) Type A Type B x 1 = 70.0 x 2 = 67.0 s1 = 3.6 s2 = 3.1 n1 = 11 n2 = 9 Determine a 99% confidence interval for the difference between the mean drying time of type A and the mean drying time of type B. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide an appropriate response. 23) The test scores of 40 students are summarized in the frequency distribution below. Find the standard deviation. 23) Score Students A) s = 11.9 B) s = 13.9 C)s = 13.2 D) s = ) The manager of a bank recorded the amount of time each customer spent waiting in line during peak business hours one Monday. The frequency distribution below summarizes the results. Find the standard deviation. Round your answer to one decimal place. 24) Waiting time (minutes) Number of customer A) 5.6 B) 7.0 C)5.3 D) 5.9 4

5 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Preliminary data analyses indicates that use of a paired t-test is reasonable. Perform the hypothesis test by using either the critical-value approach or the P-value approach as indicated. 25) Five students took a math test before and after tutoring. Their scores were as follows. 25) Subject A B C D E Before After At the 1% significance level, do the data provide sufficient evidence to conclude that the mean score before tutoring differs from the mean score after tutoring? Use the critical-value approach. 26) A coach uses a new technique in training middle distance runners. The times, in seconds, for 8 different athletes to run 800 meters before and after this training are shown below. 26) Athlete A B C D E F G H Before After At the 5% significance level, do the data provide sufficient evidence that the training helps to improve times for the 800 meters? Use the critical-value approach. Use the paired t-interval procedure to obtain the required confidence interval. You may assume that the conditions for using the procedure are satisfied. 27) Using the sample paired data below, determine a 90% confidence interval for the 27) difference between the mean of x and the mean of y. x y ) A coach uses a new technique in training middle distance runners. The times, in seconds, for 9 different athletes to run 800 meters before and after this training are shown below. 28) Athlete A B C D E F G H I Before After Determine a 99% confidence interval for the difference between the mean time before and after training. Use the one-proportion z-interval procedure to find the required confidence interval. 29) A researcher wishes to estimate the proportion of adults in the city of Darby who are vegetarian. In a random sample of 770 adults from this city, the proportion that are vegetarian is Find a 95% confidence interval for the proportion of all adults in the city of Darby that are vegetarians. 29) 30) In a sample of 713 patients who underwent a certain type of surgery, 22% experienced complications. Find a 90% confidence interval for the proportion of all those undergoing this surgery who experience complications. 30) 5

6 31) A survey of 300 union members in New York State reveals that 112 favor the Republican candidate for governor. Construct the 98% confidence interval for the proportion of all New York State union members who favor the Republican candidate. 31) Use the one-proportion z-test to perform the required hypothesis test. Use the critical-value approach. 32) A manufacturer considers his production process to be out of control when defects exceed 32) 3%. In a random sample of 85 items, the defect rate is 5.9% but the manager claims that this is only a sample fluctuation and that production is not really out of control. At the 0.01 level of significance, do the data provide sufficient evidence that the percentage of defects exceeds 3%? 33) An airline's public relations department says that the airline rarely loses passengers' luggage. It further claims that on those occasions when luggage is lost, 88% is recovered and delivered to its owner within 24 hours. A consumer group who surveyed a large number of air travelers found that only 133 out of 160 people who lost luggage on that airline were reunited with the missing items by the next day. At the 5% level of significance, do the data provide sufficient evidence to conclude that the proportion of times that luggage is returned within 24 hours is less than 0.88? 33) 34) A poll of 1,068 adult Americans reveals that 48% of the voters surveyed prefer the Democratic candidate for the presidency. At the 0.05 level of significance, do the data provide sufficient evidence that the percentage of all voters who prefer the Democrat is less than 50%? 34) Use the two-proportions z-interval procedure to obtain the required confidence interval for the difference between two population proportions. Assume that independent simple random samples have been selected from the two populations. 35) In a random sample of 43 Democrats from one city, 21 approved of the mayor's 35) performance. In a random sample of 58 Republicans from the city, 34 approved of the mayor's performance. Find a 90% confidence interval for the difference between the proportions of Democrats and Republicans who approve of the mayor's performance. 36) A survey found that 37 of 76 randomly selected women and 43 of 77 randomly selected men follow a regular exercise program. Find a 95% confidence interval for the difference between the proportions of women and men who follow a regular exercise program. 36) Use the regression equation to predict the y-value corresponding to the given x-value. Round your answer to the nearest tenth. 37) The regression equation relating dexterity scores (x) and productivity scores (y) for ten 37) randomly selected employees of a company is y^ = x. Predict the productivity score for an employee whose dexterity score is ) The regression equation relating attitude rating (x) and job performance rating (y) for ten randomly selected employees of a company is y^ = x. Predict the job performance rating for an employee whose attitude rating is ) 6

7 Answer Key Testname: FINAL EXAM REVIEW 1) The data is highly symmetrical. It is a uniform distribution. 2) The data is slightly left-skewed. 3) 9.18% 4) ) ) ) ) 1.96% 9) 3.79 to 4.51 liters 10) to hours 11) 19.3 to 20.7 ounces 12) to milligrams 13) to ) 67.7 to ) Answers will vary. Possible answer: The results are statistically significant at the 5% significance level if the null hypothesis is rejected. This means that the data provide evidence to conclude that μ 37.1 C. However, even if the results are statistically significant, this does not necessarily imply practical significance - the difference between μ and 37.1 C could be too small to be of practical importance. 16) A null hypothesis which is rejected at the 5% level of significance will certainly be rejected at the 10% level of significance but not necessarily at the 1% level of significance. If the null hypothesis is rejected at the 5% level of significance, the test statistic is greater than the critical value of This means that the test statistic is certainly greater than 1.28 which is the critical value corresponding to a 10% level of significance. The test statistic is not necessarily greater than 2.33 which is the critical value corresponding to a 1% level of significance. 17) If the null hypothesis is rejected at the 1% level of significance this provides much stronger evidence that μ > 488 than if the null hypothesis is rejected at the 10% level of significance. Suppose that his teaching method actually does not work and that μ = 488. Then the chance that the null hypothesis would be rejected at the 10% level is 10%. This is not so unlikely. However, the chance that the null hypothesis would be rejected at the 1% level is only 1%. 18) H 0 : μ = H a : μ α = 0.01 Test statistic: t = Critical values: t = , Reject the null hypothesis. At the 1% level of significance, there is sufficient evidence to conclude that the mean score for sober women differs from 35.0, the mean score for men. 19) H 0 : μ = 160. H a : μ > 160. Test statistic: t = Critical value: t = Reject the null hypothesis. At the 5% level of significance, there is sufficient evidence to conclude that the mean score for students from this university is greater than

8 Answer Key Testname: FINAL EXAM REVIEW 20) H 0 : μ = 18.7 months. H a : μ 18.7 months. Test statistic: t = Critical values: t = ± Do not reject H 0. At the 5% level of significance, there is not sufficient evidence to conclude that the mean amount of time served by convicted burglars in her hometown is different from 18.7 months. 21) to hours 22) to 7.38 hours 23) C 24) A 25) H0: μ1 = μ2 Ha: μ1 μ2 α = 0.01 t = Critical values = ±4.604 Do not reject H0. At the 1% significance level, the data do not provide sufficient evidence to conclude that the mean score before tutoring differs from the mean score after tutoring. 26) H0: μ1 = μ2 Ha: μ1 > μ2 t = Critical value = Reject H0. At the 5% significance level, the data provide sufficient evidence to conclude that the training helps to improve times for the 800 meters. 27) to ) to 3.26 seconds 29) to ) to ) to ) H0: p = 0.03 Ha: p > α = 0.01 Test statistic: z = Critical value: z = Do not reject the null hypothesis. At the 1% significance level, the data do not provide sufficient evidence to conclude that the percentage of defects exceeds 3%. 33) H0: p = 0.88; Ha: p < 0.88; Test statistic: z = Critical value = Reject H0. At the 5% level of significance, the data provide sufficient evidence to conclude that the proportion of times that luggage is returned within 24 hours is less than ) H0: p = 0.5 Ha: p < 0.5. Test statistic: z = Critical value: z = Do not reject the null hypothesis. At the 5% level of significance, the data do not provide sufficient evidence to conclude that the percentage of voters who prefer the Democrat is less than 50%. 35) to ) to ) )