Question

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 zequalsnegative 2.23. Can we conclude that Upper H 0 should be rejected at the a right parenthesis alpha equals 0.10 comma b right parenthesis alpha equals 0.05 comma and c right parenthesis alpha equals 0.01 ​level? A. ​a) yes;​ b) yes;​ c) yes B. ​a) no;​ b) no;​ c) no C. ​a) yes;​ b) yes;​ c) no D. ​a) no;​ b) no;​ c) yes

Answer 1

In this case,

Null Hypothesis, H₀ : proportion of doctors who recommend brand Z is 90%.

Alternate Hypothesis, H_a : proportion of doctors who recommend brand Z is less than​ 90%.

T stat = -2.23. At Z = -2.23, p value is 0.013. Confidence level = 98.7%

Now ,

a. at = 0.1 level, confidence levels are 90%:

In this case,  p value (0.013) is less than 0.1 , Confidence levels of Alternate Hypothesis (98.7%)

is higher than 90% . Therefore, Yes, Null Hypothesis is rejected & the alternate Hypothesis is accepted .

b. at = 0.05 level, confidence levels are 95%:

In this case,  p value (0.013) is less than 0.05 , Confidence levels of Alternate Hypothesis (98.7%)

is higher than 95%.  Therefore, Yes, Null Hypothesis is rejected & the alternate Hypothesis is accepted

c. at = 0.01 level, confidence levels are 99%:

In this case,  p value (0.013) is greater than 0.01, Confidence levels of Alternate Hypothesis (98.7%)

is higher than 99%.Therefore, No,Null Hypothesis is not rejected & the alternate Hypothesis is rejected .

Therefore, the right option would be C. a) yes;​ b) yes;​ c) no