Question

An accountant of wallie's the pizza franchise claims that its stores generate average weekly revenues of at least $7,000 per store. a potential buyer who is considering purchasing a wallie's pizza franchise is doubtful about this claim, and believes instead that the average weekly revenue might be less than $7,000. with some effort, he obtains revenues from 20 wallie's stores across the country by interviewing their managers/employees and finds that the average revenue is $6400. historical tax filings by wallie's indicate that the standard deviation of revenues has been about $1042. store revenues are assumed to be normally distribute
d.what is the calculated value of the statistic to test the potential buyer's belief at the 1% level of significance?

Answer 1

The calculated value of the Z statistic to test the potential buyer's belief at the 1% significant level is -2.57512627.

The calculated Z score is slightly greater than the critical value of -2.575, the potential buyer's view that weekly store revenues are less than $7,000 stands vindicated.

Since store revenues are assumed to be normally distributed and population standard deviation is given, we can use the Z-test. The relevant test statistic is the Z-score.

We use the following formula for calculating the Z score:

Z = (X - μ) / (σ /√n)

Substituting the relevant values we get,

Z = (6400 -7000) / (1042/√20)

Z = -600 / 232.9982833

Z = -2.57512627