Question

A salesperson in Walmart claims that 40% of all customers who come to the store make a purchase. To test this claim, a store manager randomly selected 100 people in the store and found 37 made a purchase. At the 0.01 level, determines if the sample provides sufficient evidence to support the salesperson’s claim. Hint: One Proportion, Z-test.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.4
Alternative Hypothesis, Ha: p ≠ 0.4

Rejection Region
This is two tailed test, for α = 0.01
Critical value of z are -2.58 and 2.58.
Hence reject H0 if z < -2.58 or z > 2.58

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.37 - 0.4)/sqrt(0.4*(1-0.4)/100)
z = -0.61

P-value Approach
P-value = 0.5419
As P-value >= 0.01, fail to reject null hypothesis.

Yes data supports the claim