# MATHEMATICS

Question 40 Complete the sentence: If we reject the null hypothesis, we conclude that _____ . there is not enough statistical evidence to infer that the alternative hypothesis is true there is not enough statistical evidence to infer that the null hypothesis is true the test must be repeated the test is statistically insignificant at the chosen level of significance

question 41 Which statement is an example of a null hypothesis? A. A particular industrial process manufactures windshields with an average length of 33 inches. B. The average quantity of detergent put into a box by a filling machine is not one pound. C. The shipping company’s average delivery time is different from 3 days. D. The average thickness of an aluminum sheet is not 0.03 inches, as required. Statement A Statement B Statement C Statement D

Question 42 A mail-order catalog claims that customers will receive their product within 4 days of ordering. A competitor believes this is an underestimate. State the appropriate null and alternative hypotheses to be tested by the competitor. Ho: u > 4 vs. Ha: u Ho: u > 4 vs. Ha: u = 4, where u = the average number of days until the product is received. Ho: u = 4 vs. Ha: u Ho: u Ho: u = 4 vs. Ha: u > 4, where u = the average number of days until the product is received.

Question 43 A meteorologist claims that the average high temperature for the month of August in Philadelphia, PA. is 82 degrees Fahrenheit. If the residents of Philadelphia do not believe this to be true, what hypotheses should they test? Ho: u > 82 degrees Fahrenheit vs. Ha: u Ho: u = 82 degrees Fahrenheit vs. Ha: u Ho: u 82 degrees Fahrenheit Ho: u = 82 degrees Fahrenheit vs. Ha: u does not = 82 degrees Fahrenheit Ho: u = 82 degrees Fahrenheit vs. Ha: u > 82 degrees Fahrenheit

Question 44 The manufacturer of a particular battery pack for laptop computers claims its battery packs can function for 9 hours, on the average, before having to be recharged. A competitor claims that the manufacturer’s claim is too high. A random sample of 38 battery packs was selected and placed on test. The mean functioning time before having to be recharged was 7.2 hours with a standard deviation of 1.5 hours. Perform the appropriate test of hypothesis to determine whether the competitor is correct. Test using alpha = 0.05. Calculate the test statistic and round your answer to the hundredths place. Test statistic = -9.06 Test statistic = -4.56 Test statistic = -6.79 Test statistic = -7.40 Test statistic = -3.26 Question 45 The manufacturer of a particular battery pack for laptop computers claims its battery packs can function for 9 hours, on the average, before having to be recharged. A competitor claims that the manufacturer’s claim is too high. A random sample of 37 battery packs was selected and placed on test. The mean functioning time before having to be recharged was 7.4 hours with a standard deviation of 1.7 hours. Perform the appropriate test of hypothesis to determine whether the competitor is correct. Test using alpha = 0.05. Based on the test statistic, what can you conclude? Test statistic = -7.464425433, so we should reject the manufacturer’s claim. Test statistic = -34.82352941, so we should reject the manufacturer’s claim. Test statistic = -5.724952969, so we should reject the manufacturer’s claim. Test statistic = -34.82352941, so we should not reject the manufacturer’s claim. Test statistic = -5.724952969, so we should not reject the manufacturer’s claim.

Question 46 A sample size of 150 is to be used to test the hypotheses H0: µ = 8.3 vs. Ha: µ ≠ 8.3 where µ is the true average weight of a newborn American baby. Determine the appropriate rejection region with a significance level of alpha = 0.05. Reject H0 if z >2.58 or z Reject H0 if z -2.58 Reject H0 if z >1.96 or z Reject H0 if z -1.96 Reject H0 if z >1.645 or z Reject H0 if z -1.645