Thank you very much for your help! (Statistics) For each scenario, give the foll

Question

Thank you very much for your help!

(Statistics) For each scenario, give the following and justify your answer:

(i) What kind of test 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? (z, z1-, z1-/2, t(n-1), t(n-1)1-, t(n-1)1-/2)

(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.’)

1. (1st case)- A random sample of n = 20 Lynwood 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.

2. (2nd case)- A random sample of m = 30 Fuji apples grown in Washington and an independent random sample of n = 50 Fuji apples grown in Oregon are collected, and their weights are measured.   The population variances for the weights of apples in both states are unknown. Test the null hypothesis that the average weight of Fuji apples grown in Washington is equal to the average weight of Fuji apples grown in Oregon, vs. the alternative hypothesis that the average weight of Fuji apples grown in Washington is not equal to the average weight of Fuji apples grown in Oregon.

3. (3rd case)- Thirty (30) PSU freshmen are randomly selected, and their high-school GPAs and college GPAs are recorded. Test the null hypothesis that the average high-school GPA for all PSU freshmen is equal to the average college GPA for all PSU freshmen, vs. the alternative hypothesis that the average high-school GPA for all PSU freshmen is greater than the average college GPA for all PSU freshmen.

Explanation / Answer

(Case 1)

(i) Since the population variances are known, we conduct a two-sample z test for difference in population means

(ii) Since the alternative hypothesis is that dogs (in such families) have more fleas, we conduct a one-sided upper test

(iii) Critical value is Z

(iv) Reject the null hypothesis if the test statistic is greater than the critical value.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.