Question

For the following​ information, determine whether a normal sampling distribution can be​ used, where p is the population​ proportion,

alphaα

is the level of​ significance,

ModifyingAbove p with caretp

is the sample​ proportion, and n is the sample size. If it can be​ used, test the claim.​Claim:

pgreater than or equals≥0.47

alphaαequals=0.06

Sample​ statistics:

ModifyingAbove p with caretpequals=0.40,

nequals=180

Answer 1

We are given:

Since and , therefore, we can use the normal sampling distribution.

The null and alternative hypotheses are:

Under the null hypothesis, the test statistic is:

  

Now we have to find the p-value. Using the standard normal table, we have:

Since the p-value is greater than 0.06, we, therefore, fail to reject the null hypothesis and there is insufficient evidence to conclude that the p is greater than 0.47