Question

A marketing manager of a well-known women’s clothing line has noticed that the sales of bootcut jeans were sluggish and therefore he suggested discontinuing production of bootcut jeans if the sales were less than 10% of the total quantity of jeans sold over the past six months.
A sample of 800 jeans sold during the past six months showed that 72 of them were bootcut jeans. If we wish to test if there is sufficient evidence to discontinue production of bootcut jeans, what assumption do you need to make to conduct the hypothesis test?

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.1
Alternative Hypothesis, Ha: p < 0.1

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.09 - 0.1)/sqrt(0.1*(1-0.1)/800)
z = -0.94

P-value Approach
P-value = 0.1736

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

There is not sufficient evidence to conclude that discontinue production of bootcut jeans

Assumptions:

• The sample must be reasonably random
• The sample must be less than 10% of the population
• The sample must be large enough so that:
n• pˆ and n(1 - pˆ ) ≥ 10 for a confidence interval
n• p and n(1 - p) ≥ 10 for the significance test