1) In a statistical test, we have a choice of a lefttailed test, a righttailed test, or a twotailed test. Is it the null hypothesis or the alternate hypothesis that determines which type of test is used? Explain your answer. The null hypothesis because it specifies what the level of significance of the test will be. The alternative hypothesis because it specifies the region of interest for the parameter in question. The alternative hypothesis because it specifies what the level of significance of the test will be. The null hypothesis because it specifies the region of Interest for the parameter in question 2) If we reject the null hypothesis, does this mean that we have proved it to be false beyond all doubt? Explain your answer. Yes, if we reject the null that suggests that it is false beyond all doubt. No, the test was conducted with a risk of a type I error. Yes, the test was conducted with a risk of a type I error. No, the test was conducted with a risk of a type II error. 3) The body weight of a healthy 3 monthold colt should be about = 60 kg. (Source: The Merck Veterinary Manual, a standard reference manual used in most veterinary colleges.) (a) If you want to set up a statistical test to challenge the claim that = 60 kg, what would you use for the null hypothesis H0? < 60 = 60 > 60 60 (b) In Nevada, there are many herds of wild horses. Suppose you want to test the claim that the average weight of a wild Nevada colt (3 months old) is less than 60 kg. What would you use for the alternate hypothesis H1? = 60 > 60 < 60 60 (c) Suppose you want to test the claim that the average weight of such a wild colt is greater than 60 kg. What would you use for the alternate hypothesis? = 60 > 60 60 < 60 (d) Suppose you want to test the claim that the average weight of such a wild colt is different from 60 kg. What would you use for the alternate hypothesis? > 60 = 60 60 < 60 (e) For each of the tests in parts (b), (c), and (d), would the area corresponding to the P value be on the left, on the right, or on both sides of the mean? left; both; right right; left; both left; right; both both; left; right 4) Let x be a random variable representing dividend yield of bank stocks. We may assume that x has a normal distribution with = 3.2%. A random sample of 10 bank stocks gave the following yields (in percents). 5.7 4.8 6.0 4.9 4.0 3.4 6.5 7.1 5.3 6.1 The sample mean is x = 5.38%. Suppose that for the entire stock market, the mean dividend yield is = 4.8%. Do these data indicate that the dividend yield of all bank stocks is higher than 4.8%? Use = 0.01. (a) What is the level of significance? _____ State the null and alternate hypotheses. Will you use a lefttailed, righttailed, or twotailed test? H0: = 4.8%; H1: < 4.8%; lefttailed H0: = 4.8%; H1: > 4.8%; righttailed H0: = 4.8%; H1: 4.8%; twotailed H0: > 4.8%; H1: = 4.8%; righttailed (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The Student's t, since we assume that x has a normal distribution with known . The standard normal, since we assume that x has a normal distribution with unknown . The Student's t, since n is large with unknown . The standard normal, since we assume that x has a normal distribution with known . What is the value of the sample test statistic? (Round your answer to two decimal places.) __________ (c) Find (or estimate) the Pvalue. (Round your answer to four decimal places.) ________ Sketch the sampling distribution and show the area corresponding to the Pvalue. Which of the following is correct? (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ? At the = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant. At the = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. At the = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. (e) State your conclusion in the context of the application. There is sufficient evidence at the 0.01 level to conclude that the average yield for bank stocks is higher than that of the entire stock market. There is insufficient evidence at the 0.01 level to conclude that the average yield for bank stocks is higher than that of the entire stock market. 5) Consider a test for . If the Pvalue is such that you can reject H0 at the 5% level of significance, can you always reject H0 at the 1% level of significance? Explain your answer. No. If the Pvalue lies between 0.01 and 0.05 you would reject at the 5% level of significance, but not at the 1% level. No. If the Pvalue lies above 0.01 you would reject at the 5% level of significance, but not at the 1% level. No. If the Pvalue lies above 0.05 you would reject at the 5% level of significance, but not at the 1% level. Yes. If H0 is rejected at the 5% level it will always be rejected at the 1% level. 6) Weatherwise is a magazine published by the American Meteorological Society. One issue gives a rating system used to classify Nor'easter storms that frequently hit New England and can cause much damage near the ocean. A severe storm has an average peak wave height of = 16.4 feet for waves hitting the shore. Suppose that a Nor'easter is in progress at the severe storm class rating. Peak wave heights are usually measured from land (using binoculars) off fixed cement piers. Suppose that a reading of 32 waves showed an average wave height of x = 17.3 feet. Previous studies of severe storms indicate that = 3.5 feet. Does this information suggest that the storm is (perhaps temporarily) increasing above the severe rating? Use = 0.01. (a) What is the level of significance? State the null and alternate hypotheses. H0: = 16.4 ft; H1: > 16.4 ft H0: = 16.4 ft; H1: 16.4 ft H0: < 16.4 ft; H1: = 16.4 ft H0: > 16.4 ft; H1: = 16.4 ft H0: = 16.4 ft; H1: < 16.4 ft (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The standard normal, since the sample size is large and is known. The standard normal, since the sample size is large and is unknown. The Student's t, since the sample size is large and is known. The Student's t, since the sample size is large and is unknown. What is the value of the sample test statistic? (Round your answer to two decimal places.) ______________ (c) Find the Pvalue. (Round your answer to four decimal places.) ________ Sketch the sampling distribution and show the area corresponding to the Pvalue. (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ? At the = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant. At the = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. At the = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. (e) Interpret your conclusion in the context of the application. There is sufficient evidence at the 0.01 level to conclude that the storm is increasing above the severe rating. There is insufficient evidence at the 0.01 level to conclude that the storm is increasing above the severe rating. 7) Consider a binomial experiment with n trials and r successes. To construct a test for a proportion p, what value do we use for the sample test statistic? r / n 2r / n (r / n)2 n / r 1) In a statistical test, we have a choice of a lefttailed test, a righttailed test, or a twotailed test. Is it the null hypothesis or the alternate hypothesis that determines which type of test is used? Explain your answer. The null hypothesis because it specifies what the level of significance of the test will be. The alternative hypothesis because it specifies the region of interest for the parameter in question. The null hypothesis because it specifies the region of Interest for the parameter in question 5) Consider a test for . If the Pvalue is such that you can reject H0 at the 5% level of significance, can you always reject H0 at the 1% level of significance? Explain your answer. No. If the Pvalue lies between 0.01 and 0.05 you would reject at the 5% level of significance, but not at the 1% level. No. If the Pvalue lies above 0.01 you would reject at the 5% level of significance, but not at the 1% level. No. If the Pvalue lies above 0.05 you would reject at the 5% level of significance, but not at the 1% level. Yes. If H0 is rejected at the 5% level it will always be rejected at the 1% level