Hypothesis Testing and Finding P-Value

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?