Question

A survey claims that 59 out of 100 customers recommend Company A for pharmacy issues. To test this claim, a random sample of 120 customers is obtained from the list of rewards customers. Of these 120 customers, 81 indicate that they recommend using Company A for pharmacy needs. We would like to know if the original claim is accurate. State your conclusion using alpha = 0.05.

Group of answer choices

The null hypothesis can be rejected: there is evidence that more than 59% of customers recommend Company A for pharmacy issues.

The null hypothesis cannot be rejected: there is evidence that the percentage of customers who recommend Company A for pharmacy issues is not equal to 75%.

The null hypothesis cannot be rejected: there is evidence that 59% of customers recommend Company A for pharmacy issues.

The null hypothesis can be rejected: there is evidence that less than 75% of customers recommend Company A for pharmacy issues.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.59
Alternative Hypothesis, Ha: p ≠ 0.59

Rejection Region
This is two tailed test, for α = 0.05
Critical value of z are -1.96 and 1.96.
Hence reject H0 if z < -1.96 or z > 1.96

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.675 - 0.59)/sqrt(0.59*(1-0.59)/120)
z = 1.89

P-value Approach
P-value = 0.0588
As P-value >= 0.05, fail to reject null hypothesis.

The null hypothesis cannot be rejected: there is evidence that 59% of customers recommend Company A for pharmacy issues.