1. For each scenario, give the following and justify your answer: What kind ofte
ID: 3203542 • Letter: 1
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1. For each scenario, give the following and justify your answer: What kind oftest should you perform? (One-sample z-test, one-sample t-test, two-sample z-test, two-sample t-test, paired t-test) (ii) Should you perform a one-sided upper, one-sided lower, or two-sided test? (iii) What is the critical value? (za, z ton-1)1.a2) z1-a/2, tin-1)a, ton-1)1-a (iv) For what values of the test statistic would you reject the null hypothesis (e.g., "Reject the null hypothesis if the test statistic is [less than, greater than, greater than in absolute value] the critical value a. (4 points) A random sample of n 20 Corvallis families with one dog and one cat is obtained, and the number of fleas found on each animal is measured. The population variances for the number of fleas on dogs and cats are both known. Test the null hypothesis that the average number of fleas on dogs (in such families) is equal to the average number of fleas on cats (in such families), vs. the alternative hypothesis that dogs (in such families) have more fleas.Explanation / Answer
a) i) Sample Size = 20 Population variances are known But Sample size is not more than 30 Also there are two samples, one of cats and one of dogs Hence we use the two sample t-test ii) Let 0 = Average number of fleas on dogs Let 1 = Average number of fleas on dogs We want to test H0 : 0 = 1 against H1 : 0 > 1 Since alternative hypothesis is for testing only 'more than' we should perform one sided test Since alternative hypothesis tests greater than (not less than) we use the one-sided upper t-test iii) Let confidence level = Degrees of freedom = n - 1 where n is the sample size Critical value for this one sided two sample t-test with confidence level is t(n-1), (1-) iv) Reject the null hypothesis if the test statistic is GREATER THAN the critical value b) i) Sample Size = 30 Population variances are not known Also Sample size is not more than 30 Also there are two samples, one is school GPA scores and other is college GPA scores Hence we use the two sample t-test ii) Let 0 = Average High School GPA Let 1 = Average College GPA We want to test H0 : 0 = 1 against H1 : 0 > 1 Since alternative hypothesis is for testing only 'more than' we should perform one sided test Since alternative hypothesis tests greater than (and not less than) we use the one-sided upper t-test iii) Let confidence level = Degrees of freedom = n - 1 where n is the sample size Critical value for this one sided two sample t-test with confidence level is t(n-1), (1-) iv) Reject the null hypothesis if the test statistic is GREATER THAN the critical value
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