It isn't clear to me that the test should be one-sided, but other than that it looks fine.
Although 85% of the general public is right-handed, a survey of 300 chief executive officers of large corporations found that 96% were right-handed.
a) Is this difference in percentages statistically significant? Test using α = 0.01.
b) Find the p-value for the test and explain what it means.
Attempt At Solution
a) The rejection region is {z > 2.33}.
Using the test:
z = (p - p0)/(sqrt(p0*(1-p0)/n), where p0 = .85, p = .96, and n = 300
I got z = 5.34. Since 5.34 > 2.33, this lies in the rejection region and thus, the difference is significant.
b) p-value = P(Z > 5.34) = 0.000000287
Since this value is so small, it is evident that the null hypothesis should be rejected.
Is this correct?