## (solution) MA260 - Statistical Analysis

A manufacturer claims that the mean amount of juice in its 16 ounce bottles is 16.1 ounces. A consumer advocacy group wants to perform a hypothesis test to determine whether the mean amount is actually less than this. The mean volume of juice for a random sample of 70 bottles was 15.94 ounces. Do the data provide sufficient evidence to conclude that the mean amount of juice for all 16-ounce bottles, µ, is less than 16.1 ounces? Perform the appropriate hypothesis test using a significance level of 0.10. Assume that s = 0.9 ounces.  A.The z of - 1.49 provides sufficient evidence to conclude that the mean amount of juice is less than 16.1 oz.B.The z of - 1.49 does not provide sufficient evidence to conclude that the mean amount of juice is less than 16.1 oz.C.The z of - 0.1778 does not provide sufficient evidence to conclude that the mean amount of juice is less than 16.1 oz.D.The z of - 0.1778 provides sufficient evidence to conclude that the mean amount of juice is less than 16.1 oz. Question 2 of 40 2.5 PointsIn 1990, the average duration of long-distance telephone calls originating in one town was 9.4 minutes. A long-distance telephone company wants to perform a hypothesis test to determine whether the average duration of long-distance phone calls has changed from the 1990 mean of 9.4 minutes. The mean duration for a random sample of 50 calls originating in the town was 8.6 minutes. Does the data provide sufficient evidence to conclude that the mean call duration, µ, is different from the 1990 mean of 9.4 minutes? Perform the appropriate hypothesis test using a significance level of 0.01. Assume that s = 4.8 minutes.A. With a z of -1.2 there is sufficient evidence to conclude that the meanvalue has changed from the 1990 mean of 9.4 minutes.B. With a P-value of 0.2302 there is not sufficient evidence to concludethat the mean value is less than the 1990 mean of 9.4 minutes.C. With a P-value of 0.2302 there is sufficient evidence to conclude thatthe mean value is less than the 1990 mean of 9.4 minutes.D. With a z of –1.2 there is not sufficient evidence to conclude that themean value has changed from the 1990 mean of 9.4 minutes. At one school, the mean amount of time that tenth-graders spend watching television each week is 18.4 hours. The principal introduces a campaign to encourage the students to watch less television. One year later, the principal wants to perform a hypothesis test to determine whether the average amount of time spent watching television per week has decreased.Formulate the null and alternative hypotheses for the study described.A.Ho: µ = 18.4 hours H a : µ ¹ 18.4 hoursB.Ho: µ = 18.4 hours H a : µ < 18.4 hoursC.Ho: µ ³ 18.4 hours H a : µ < 18.4 hoursD.Ho: µ = 18.4 hours H a : µ > 18.4 hours The owner of a football team claims that the average attendance at home games is over 4000, and he is therefore justified in moving the team to a city with a larger stadium. Assume that a hypothesis test of the claim has been conducted and that the conclusion of the test was to reject the null hypothesis. Identify the population to which the results of the test apply.A. All games played by the team in question in which the attendance is over 4000B. All future home games to be played by the team in questionC. All home games played by the team in questionD. None of the populations given are appropriateA two-tailed test is conducted at the 5% significance level. Which of the z-scores below is the smallest one that leads to rejection of the null hypothesis?A. 1.12B. 1.48C. 1.84D. 2.15A two-tailed test is conducted at the 5% significance level. What is the left tail percentile required to reject the null hypothesis?A. 97.5%B. 5%C. 2.5%D. 95%A psychologist claims that more than 19 percent of the population suffers from professional problems due to extreme shyness. Assume that a hypothesis test of the claim has been conducted and that the conclusion of the test was to reject the null hypothesis. Identify the population to which the results of the test apply.A. The population is all shy workers.B. The population cannot be identified from the description of the study.C. The population is all American workers.D. The population is all American professional workers (doctors, lawyers, CPA’s, and the like..In the past, the mean running time for a certain type of flashlight battery has been 9.8 hours. The manufacturer has introduced a change in the production method and wants to perform a hypothesis test to determine whether the mean running time has increased as a result. The hypotheses are:H0 : µ = 9.8 hoursHa : µ > 9.8 hoursSuppose that the results of the sampling lead to rejection of the null hypothesis. Classify that conclusion as a Type I error, a Type II error, or a correct decision, if in fact the mean running time has not increased.A. Type I errorB. Type II errorC. Correct decisionD. Can not be determined from this informationA study of a brand of “in the shell peanuts” gives the following results:A significant event at the 0.01 level is a fan getting a bag with how many peanuts? No dataA. 30 peanutsB. 25 or 30 peanutsC. 25 or 55 peanutsD. 25 peanutsThe principal of a middle school claims that annual incomes of the families of the seventh-graders at his school vary more than the annual incomes of the families of the seventh-graders at a neighboring school, which have variation described by s = \$13,700. Assume that a hypothesis test of the claim has been conducted and that the conclusion of the test was to reject the null hypothesis. Identify the population to which the results of the test apply.A. The current seventh graders at the principal’s schoolB. Seventh graders’ families at the school with a standard deviation of \$13,700C. All of the families of the class of seventh graders at the principal’s schoolD. All seventh graders’ familiesIn the past, the mean running time for a certain type of flashlight battery has been 8.0 hours. The manufacturer has introduced a change in the production method and wants to perform a hypothesis test to determine whether the mean running time has increased as a result. The hypotheses are:H0 : µ = 8.0 hoursHa : µ > 8.0 hoursExplain the meaning of a Type II error.A. Concluding that µ > 8.0 hours when in fact µ > 8.0 hoursB. Failing to reject the hypothesis that µ = 8.0 hours when in fact µ >8.0 hoursC. Concluding that µ > 8.0 hoursD. Failing to reject the hypothesis that µ = 8.0 hours when in fact µ = 8.0 hoursA poll of 1,068 adult Americans reveals that 52% of the voters surveyed prefer the Democratic candidate for the presidency. At the 0.05 significance level, test the claim that more than half of all voters prefer the Democrat.A. Reject the null hypothesis. Conclude that there is insufficient evidence that more than half of all voters prefer Democrats.B. Do not reject the null hypothesis. Conclude that there is sufficient evidence that more than half of all voters prefer Democrats.C. Reject the null hypothesis. Conclude that there is sufficient evidence that more than half of all voters prefer Democrats.D. Do not reject the null hypothesis. Conclude that there is insufficient evidence that more than half of all voters prefer Democrats.A two-tailed test is conducted at the 5% significance level. What is the P-value required to reject the null hypothesis?A. Greater than or equal to 0.10B. Less than or equal to 0.05C. Less than or equal to 0.10D. Greater than or equal to 0.05 A long-distance telephone company claims that the mean duration of long-distance telephone calls originating in one town was greater than 9.4 minutes, which is the average for the state. Determine the conclusion of the hypothesis test assuming that the results of the sampling do not lead to rejection of the null hypothesis.A. Conclusion: Support the claim that the mean is less than 9.4 minutes.B. Conclusion: Support the claim that the mean is greater than 9.4 minutes.C. Conclusion: Support the claim that the mean is equal to 9.4 minutes.D. Conclusion: Do not support the claim that the mean is greater than 9.4 minutes.A nationwide study of American homeowners revealed that 65% have one or more lawn mowers. A lawn equipment manufacturer, located in Omaha, feels the estimate is too low for households in Omaha. Find the P-value for a test of the claim that the proportion with lawn mowers in Omaha is higher than 65%. Among 497 randomly selected homes in Omaha, 340 had one or more lawn mowers. Use Table 5.1 to find the best answer.A. 0.0559B. 0.1118C. 0.0252D. 0.0505A researcher wants to check the claim that convicted burglars spend an average of 18.7 months in jail. She takes a random sample of 35 such cases from court files and finds that months. Assume that the population standard deviation is 7 months. Test the null hypothesis that µ = 18.7 at the 0.05 significance level. No dataA.Do not reject the null hypothesis and conclude that the claim that the mean is different from 18.7 months is supported.B.Do not reject the null hypothesis and conclude that the claim that the mean is different from 18.7 months cannot be supported.C.Reject the null hypothesis and conclude that the claim that the mean is different from 18.7 months is supported.D.Reject the null hypothesis and conclude that the claim that the mean is different from 18.7 months cannot be supported.In 1990, the average duration of long-distance telephone calls originating in one town was 9.3 minutes. A long-distance telephone company wants to perform a hypothesis test to determine whether the average duration of long-distance phone calls has changed from the 1990 mean of 9.3 minutes. Formulate the null and alternative hypotheses for the study described.A.Ho: µ = 9.3 minutes H a : µ < 9.3 minutesB.Ho: µ = 9.3 minutes H a : µ > 9.3 minutesC.Ho: µ = 9.3 minutes H a : µ ¹ 9.3 minutesD.Ho: µ ¹ 9.3 minutes H a : µ = 9.3 minutesQuestion 18 of 40 2.5 Pointswithout computing a P-value, determine whether the alternate hypothesis is supported and give a reason for your conclusion. No dataA.is less than 1 standard deviation above the claimed mean.B.is more than 4 standard deviations above the claimed mean.C.is less than 1 standard deviation above the claimed mean.D.is more than 4 standard deviations above the claimed mean.The owner of a football team claims that the average attendance at home games is over 3000, and he is therefore justified in moving the team to a city with a larger stadium. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is failure to reject the null hypothesis, state the conclusion in non-technical terms.A. There is sufficient evidence to support the claim that the mean attendance is greater than 3000.B. There is sufficient evidence to support the claim that the mean attendance is equal to 3000.C. There is not sufficient evidence to support the claim that the mean attendance is greater than 3000.D. There is not sufficient evidence to support the claim that the mean attendance is less than 3000.Reset SelectionA two-tailed test is conducted at the 0.10 significance level. What is the P-value required to reject the null hypothesis?A. Greater than or equal to .010B. Greater than or equal to 0.05C. Less than or equal to 0.10D. Less than or equal to 0.05A golfer wished to find a ball that would travel more than 180 yards when hit with his 5-iron with a club speed of 90 miles per hour. He had a golf equipment lab test a low compression ball by having a robot swing his club 7 times at the required speed. State the null and alternative hypotheses for this test.A.H0: µ = 180; Ha: µ > 180B.H0: µ > 180; Ha: µ > 180C.H0: µ < 180; Ha: µ > 180D.H0: µ = 180; Ha: µ < 180One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent. The following counts were observed. Colorblind Not Colorblind TotalMale 8 52 60Female 2 38 40Total 10 90 100Find the value of the X2 statistic for the data above.A. 1.463B. 1.852C. 1.947D. 1.949A golfer wished to find a ball that would travel more than 160 yards when hit with his 7-iron with a club speed of 90 miles per hour. He had a golf equipment lab test a low compression ball by having a robot swing his club 8 times at the required speed. State the null and alternative hypotheses for this test.A.H0: µ = 160; Ha: µ > 150B.H0: µ = 150; Ha: µ > 150C.H0: µ = 160; Ha: µ > 160D.H0: µ = 140; Ha: µ > 160A golfer wished to find a ball that would travel more than 180 yards when hit with his 5-iron with a club speed of 90 miles per hour. He had a golf equipment lab test a low compression ball by having a robot swing his club 7 times at the required speed.Data from this test resulted in a sample mean of 184.2 yards and a sample standard deviation of 5.8 yards. Assuming normality, carry out a hypothesis test at the 0.05 significance level to determine whether the ball meets the golfer’s requirements. Use the partial t-table below. Area in one tail 0.025 0.05 Area in two tails Degrees ofFreedomn - 1 0.05 0.106 2.447 1.9437 2.365 1.8958 2.306 1.8609 2.262 1.833A.Reject the null hypothesis. The data do not provide sufficient evidence that the average distance is greater than 180 yards.B. Reject the null hypothesis. The data do provide sufficient evidence that the average distance is greater than 180 yards.C. Do not reject the null hypothesis. The data do provide sufficient evidence that the average distance is greater than 180 yards.D. Do not reject the null hypothesis. The data do not provide sufficient evidence that the average distance is greater than 180 yards.One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent.The critical value of X2 for a 2 x 2 table using a 0.05 significance level is 3.841. If the value of the X2 statistic is 3.179, state your conclusion about the relationship between gender and colorblindness.A.Do not reject H0.B.Reject H0.C.There is sufficient evidence to support the claim that gender and colorblindness are not related.D.There is not sufficient evidence to accept or reject H0.A 95% confidence interval for the mean of a normal population is found to be 15.6 < µ < 24.8. What is the margin of error?A. 4.4B. 4.6C. 4.8D. 5.0The margin of error in estimating the population mean of a normal population is E = 9.3 when the sample size is 15. If the sample size had been 18 and the sample standard deviation did not change, would the margin of error be larger or smaller than 9.3? Explain your answer.A. Smaller. E decreases as the square root of the sample size gets larger.B. Smaller. E increases as the square root of the sample size gets larger.C. Larger. E decreases as the square root of the sample size gets larger.D. Larger. E increases as the square root of the sample size gets larger.The following data were analyzed using one-way analysis of variance.A B C34 27 1926 23 2131 29 2228 21 12Which one of the following statements is correct?A. The purpose of the analysis is to determine whether the groups A, B, and C are independent.B. The purpose of the analysis is to test the hypothesis that the population means of the three groups are equal.C. The purpose of the analysis is to test the hypothesis that the population variances of the three groups are equal.D. The purpose of the analysis is to test the hypothesis that the sample means of the three groups are equal.A large test statistic F tells us that the sample means __________ the data within the individual samples, which would be unlikely if the populations means really were equal (as the null hypothesis claims).A. differ more thanB. differ less thanC. are equal toD. do not vary withOne hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent. The following counts were observed. Colorblind Not Colorblind TotalMale 7 53 60Female 1 39 40Total 8 92 100State the null and alternative hypothesis for the information above.A.H0: Colorblindness and gender are dependent characteristics.Ha: Colorblindness and gender are related in some way.B.H0: Colorblindness and gender are independent characteristics.Ha: Colorblindness and gender are not related in any way.C.H0: Colorblindness and gender are dependent characteristics.Ha: Colorblindness and gender are not related in any way.D.H0: Colorblindness and gender are independent characteristics.Ha: Colorblindness and gender are related in some way.A 95% confidence interval for the mean of a normal population is found to be 15.6 < µ < 25.2. What is the margin of error?A. 3.9B. 4.8C. 4.9D. 3.7Which of the following statements is true?A. The t distribution cannot be used when finding a confidence interval for the population mean with a small sample whenever the sample comes from a symmetric population.B. The t distribution can be used when finding a confidence interval for the population mean with a small sample whenever the sample comes from a symmetric population.C. The p distribution can be used when finding a confidence interval for the population mean with a small sample whenever the sample comes from a symmetric population.D. The p distribution can be used when finding a confidence interval for the population mean with a small sample whenever the sample comes from a symmetric population.A 95% confidence interval for the mean of a normal population is found to be 17.6 < µ < 23.6. What is the margin of error?A. 2.0B. 2.7C. 3.0D. 4.0The following data were analyzed using one-way analysis of variance.A B C34 27 1926 23 3131 29 2228 21 22Which one of the following statements is correct?A.The purpose of the analysis is to determine whether the groups A, B, and C are independent.B. The purpose of the analysis is to test the hypothesis that the population means of the three groups are equal.C. The purpose of the analysis is to test the hypothesis that the population variances of the three groups are equal.D. The purpose of the analysis is to test the hypothesis that the sample means of the three groups are equal.One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent.The critical value of X2 for a 2 x 2 table using a 0.05 significance level is 3.841. If the value of the X2 statistic is 4.613, state your conclusion about the relationship between gender and colorblindness.A.Reject H0. There is not sufficient evidence to support the claim that gender and colorblindness are related.B.Reject H0. There is sufficient evidence to support the claim that gender and colorblindness are related.C.Do not Reject H0. There is sufficient evidence to support the claim that gender and colorblindness are related.D.Do not Reject H0. There is not sufficient evidence to support the claim that gender and colorblindness are related.A simple random sample from a normal distribution is taken in order to obtain a 95% confidence interval for the population mean. If the sample size is 8, the sample mean x̄ is 22, and the sample standard deviation s is 6.3, what is the margin of error? Show your answer to 2 decimal places.A. df = 7; E = 3.3445.38 = 5.6566B. df = 8; E = 3.3445.38 = 5.6566C. df = 6; E = 2.3656.38 = 5.769D. df = 7; E = 2.365 6.38 = 5.869One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent.The critical value of X2 for a 2 x 2 table using a 0.05 significance level is 3.841. If the value of the X2 statistic is 3.427, state your conclusion about the relationship between gender and colorblindness.A.Do not reject H0. There is not sufficient evidence to support the claim that gender and colorblindness are related.B.Do not reject H0. There is sufficient evidence to support the claim that gender and colorblindness are related.C.Reject H0. There is not sufficient evidence to support the claim that gender and colorblindness are related.D.Reject H0. There is sufficient evidence to support the claim that gender and colorblindness are related.A 95% confidence interval for the mean of a normal population is found to be 13.2 < µ < 22.4. What is the margin of error?A. 4.6B. 4.4C. 4.2D. 5.6One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent. The following counts were observed. Colorblind Not Colorblind TotalMale 7 53 60Female 1 39 40Total 8 92 100If gender and colorblindness are independent, find the expected values corresponding to the male combinations of gender and colorblindness.A. Colorblind Male 4.8; Not Colorblind Male 55.2B. Colorblind Male 6.8; Not Colorblind Male 53.2C. Colorblind Male 4.8; Not Colorblind Male 55.4D. Colorblind Male 4.8; Not Colorblind Male 56.2One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent. The following counts were observed. Colorblind Not Colorblind TotalMale 8 52 60Female 2 38 40Total 10 90 100State the null and alternative hypothesis for the test associated with this data.A.H0: Colorblindness and gender are dependent characteristics.Ha: Colorblindness and gender are not related in any way.B.H0: Colorblindness and gender are dependent characteristics.Ha: Colorblindness and gender are related in some way.C.H0: Colorblindness and gender are independent characteristics.Ha: Colorblindness and gender are not related in any way.D.H0: Colorblindness and gender are independent characteristics.Ha: Colorblindness and gender are related in some way.

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