56-57 We are doing an experiment where we record the number of heads when we get

Question

56-57 We are doing an experiment where we record the number of heads when we get when we unbiased coin many times. For what sample sizes below would the sampling distribution of sample proportion be approximately normally distributed? a) 5 b) 28 c) 50 d) All of the above e) None of the above For a test with the null hypothesis Ho: p = 0.5 vs. the alternative Ha: p> 0.5, the null hypothesis was not rejected at level alpha = .05. Das wants to perform the same test at level alpha = .025. What will be his conclusion? a) eject H_0. b) Fail to Reject H_0. c) No conclusion can be made. d) Reject Ha. The null hypothesis Ho: p = .5 against the alternative Ha: p > .5 was rejected at level alpha = 0.01. Nate wants to know what the test will result at level alpha = 0.10. What will be his conclusion? e) Reject H_0. Fail to Reject H_0. g) No conclusion can be made. h) Reject Ha.

Explanation / Answer

56.Alpha = 0.05; Null hypothesis was not rejected ;

Null hypothesis is not rejected when p-value > Alpha; As the null hypothesis was not rejected; the p-value is greater than 0.05;

Das wants to perform the same test i.e p-value is same as the above and we know that p-value is > 0.05 . so if , p-value is greater than 0.05 then p-value is definitely greater than level alpha =0.025 also. Then the null hypothesis is not rejected i.e Fail to reject null hypothesis.

Ans :  Fail to reject null hypothesis.

57. Null hypothesis was rejected at level alpha = 0.01; that means p-value is less than 0.01;

Nate wants to know the test result at level alpha = 0.10; p-value is the same for this test too; From above we konw that p-value is less than 0.01; if p-value is less than 0.01 then p-value is definitely less than 0.10; Since p-value is less than alpha = 0.10; Reject null hypothesis.

Ans : Reject null hypothesis.

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