Hypothesis Testing Quiz Solutions, Exams of Mathematics

Download Hypothesis Testing Quiz Solutions and more Exams Mathematics in PDF only on Docsity! MATH221 Week 6 Quiz A company claims that its heaters last at most 5 years. Write the null and alternative hypotheses. - Ho: μ = 5, Ha: μ > 5 An executive claims that her employees spend no less than 2.5 hours each week in meetings. Write the null and alternative hypotheses. - Ho: μ = 2.5, Ha: μ < 2.5 Which of the following is possibly a valid outcome of a hypothesis test: - Reject Ho A landscaping company claims that at least 90% of workers arrive on time. If a hypothesis test is performed that rejects the null hypothesis, how would this decision be interpreted? - There is not sufficient evidence to support the claim that at least 90% of workers arrive on time A textbook company claims that their book is so engaging that less than 55% of students read it. If a hypothesis test is performed that fails to reject the null hypothesis, how would this decision be interpreted? - There is not sufficient evidence to support the claim that less than 55% of students read this text An advocacy group claims that the mean braking distance of a certain type of tire is 75 feet when the car is going 40 miles per hour. In a test of 45 of these tires, the braking distance has a mean of 77 and a standard deviation of 5.9 feet. Find the standardized test statistic and the corresponding p-value. - test statistic = 2.27, p-value = 0.0230 The heights of 82 roller coasters have a mean of 285.2 feet and a standard deviation of 59.3 feet. Find the standardized test statistics and the corresponding p-value when the claim is that roller coasters are less than 290 feet tall. - test statistic = -0.73, p-value = 0.2328 Which of the following would be a valid alternative hypothesis in a right-tail test? - Ha: mean > 17 What would be the result of a hypothesis test where test-statistic=1.00, p-value=0.1599 and α=.10? - Do not reject Ho since p-value is not less than α A manufacturer claims that their calculators are 6.800 inches long. A random sample of 39 of their calculators finds they have a mean of 6.812 inches with a standard deviation of 0.03 inches. At α=0.08, can you support the manufacturer's claim using the p value? - Claim is the null hypothesis, reject the null hypothesis and cannot support claim as p-value (0.012) is less than alpha (0.08) A travel analyst claims that the mean room rates at a three-star hotel in Chicago is greater than $152. In a random sample of 36 three-star hotel rooms in Chicago, the mean room rate is $160 with a population standard deviation of $41. At α=0.10, can you support the analyst's claim using the p-value? - Claim is the alternative hypothesis, fail to reject the null hypothesis as p-value (0.121) is not less than alpha (0.10), and cannot support the claim In a hypothesis test, the claim is μ>1137. A sample 50 has a mean of 1114.67 and a population standard deviation of 20.3 from a normally distributed data set. In this hypothesis test, would a z test statistic be used or a t test statistic and why? - z test statistic would be used as the population standard deviation is known What type of test would you perform for the following hypotheses: Ho: μ = 23, Ha: μ ≠ 23 - Two-tail test A used car dealer says that the mean price of a three-year-old sport utility vehicle in good condition is $18,000. A random sample of 20 such vehicles has a mean price of $18,450 and a standard deviation of $1930. At α=0.08, can the dealer's claim be supported assuming the population is normally distributed? - Yes, since the p-value of 0.310 is greater than alpha of 0.08, the null is not rejected. The claim is the null, so is supported