1.Several years ago, a government agency reported the default rate (the proporti
ID: 3203618 • Letter: 1
Question
1.Several years ago, a government agency reported the default rate (the proportion of borrowers who default on their loans)
on a certain type of loan at . Set up the null and alternative hypotheses to determine if the default rate this year is 0.045 different from 0.045
What are the correct null and alternative hypotheses to test the claim that the default rate is different this year?
A. H0: p 0.045
Ha: p = 0.045
B. H0: p > 0.045
Ha: p = 0.045
C. H0: p = 0.045
Ha: p > 0.045
D. H0: p = 0.045
Ha: p 0.045
E. H0: p < 0.045
Ha: p = 0.045
F. H0: p = 0.045
Ha: p < 0.045
2. A university economist conducted a study of elementary school lunch menus. During the state-mandated testing period, school lunches averaged 887 calories. The economist claimed that after the testing period ended, the average caloric content of the school lunches increased significantly. Set up the null and alternative hypothesis to test the economist's claim.
Choose the correct answer below.
A. H0: = 887, Ha: 887
B. H0: = 887, Ha: > 887
C. H0: 887, Ha: > 887
D. H0: = 887, Ha: < 887
3. For the and observed significance level (p-value) pair, indicate whether the null hypothesis would be rejected.
= 0.01, p-value = 0.001
Choose the correct conclusion below.
A. Do not reject the null hypothesis since the p-value is not less than the value of .
B. Reject the null hypothesis since the p-value is less than the value of .
C. Do not reject the null hypothesis since the p-value is less than the value of .
D. Reject the null hypothesis since the p-value is not less than the value of .
Explanation / Answer
1) The correct answer choice is D. This is because we want to test if the current value of p is different from p=0.045. The null hypothesis expresses the current beliefs about the parameter p. When we want to test whether p is different from 0.045 we want to assure that the probability that p=0.045 is rejected wrongly is as low as possible. We will set the maximum permissible value for this probability as our level of significance. The alternate is what we suspect is the real scenario. That is p is different from 0.045 (it may be more/less but different)
2) The correct answer choice is B. Again as with the previous answer welike to set the null hypothesis to be a conservative(statistically) viewpoint that the value has not changed. The alternative is our( in this case the economist's) suspicion that the average calorie consumption has increased and is hence greater than 887.
3) the correct answer choice is B. The p-value is the largest level of significance that fails to reject the null hypothesis. That is if any level of significance is greater than the p-value, the null hypothesis is rejected.
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