Question

Question 14 1 pts A survey claims that 9 out of 10 doctors (i.e., 90%) recommend brand Z for their patients who have children. To test this claim against the alternative that the actual proportion of doctors who recommend brand Z is less than 90%, a random sample of doctors was taken. Suppose the test statistic is z- -2.23. Can we conclude that the null hypothesis should be rejected at the a) a =0.10, b) a = 0.05, and c) a =0.01 level? a) yes: b) yes: clyes a) yes: b) yes:c) no a) no: b) no c) no a) no; b) no; c) yes

Answer 1

Given that in a survey X = 9 out of N = 10 doctors recomment brand Z for their parents who have children. Now to test the claim an alternate hypothesis is created that the proportion is less than 0.90 , hence based on the claim and alternate hypothesis the hypotheses are:

Ho: P = 0.90

Ha: P< 0.90

Now the Z score is computed as -2.23.

Rejection region:

Reject the Ho if P-value is than the significance level.

P-value:

The P-value is compute dusing the excel formula for normal distribution which is =NORM.S.DIST(-2.23, TRUE), thus the P-value is computed as 0.0129.

Conclusion:

Since the P-value is less than 0.01 hence we can reject the Ho at 0.10 and also at 0.05 becuse the p-value is less than 0.05 but the p-value is greater than 0.01 hence we fail to reject Ho at 0.01 level of significance.

Hence the correct option is:

a) yes, b) yes, c) No