# mathematics

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 0.10 B. Less than or equal to 0.05 C. Less than or equal to 0.10 D. 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. 0.0559 B. 0.1118 C. 0.0252 D. 0.0505 A 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. A. 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 [removed] 9.3 minutes C. Ho: µ = 9.3 minutes H a : µ ¹ 9.3 minutes D. Ho: µ ¹ 9.3 minutes H a : µ = 9.3 minutes Question 18 of 40 2.5 Points without computing a P-value, determine whether the alternate hypothesis is supported and give a reason for your conclusion. A. 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 Selection A 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 .010 B. Greater than or equal to 0.05 C. Less than or equal to 0.10 D. Less than or equal to 0.05 A 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 > 180 B. H0: µ > 180; Ha: µ > 180 C. H0: µ [removed] 180 D. H0: µ = 180; Ha: µ [removed] 150 B. H0: µ = 150; Ha: µ > 150 C. H0: µ = 160; Ha: µ > 160 D. H0: µ = 140; Ha: µ > 160 A 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 of Freedom n – 1 0.05 0.10 6 2.447 1.943 7 2.365 1.895 8 2.306 1.860 9 2.262 1.833 A. 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. 4.4 B. 4.6 C. 4.8 D. 5.0 The 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 C 34 27 19 26 23 21 31 29 22 28 21 12 Which 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 than B. differ less than C. are equal to D. do not vary with