Statistics Question

Question

A company took a survey asking the employees if they were satisfied with the health Coverage package provided. Of 200 employees surveyed 124 responded YES

The 90% CI for the YES is between 56.5 to 67.5%

Standard error = .0343

Using that sample information, can be proven that the % of YES is greater than or equal to 60%?

--> alternate hypothesis is greater than 60%

What is the standard error?

Answer 1

The null hypothesis is that the %yes is equal to 60% (0.6).

If the value specified in the null hypothesis is within the bounds of the confidence interval you CANNOT reject the null hypothesis at the given level of confidence (90% or level of significance alpha = 0.10).

phat = 124/200 = 0.62.

standard error = sqrt(phat*(1-phat))/n) = sqrt(0.62*0.38/200) = 0.0343