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

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