Question

An entrepreneur is considering the purchase of a coin-operated laundry. The current owner claims that over the past 5 years, the average daily revenue was $675 with a standard deviation of $75. A sample of 30 days reveals a daily average revenue of $625. If you were to test the null hypothesis that the daily average revenue was $675 and decide not to reject the null hypothesis, what can you conclude

Answer 1

We conclude that the daily average revenue was actually $675.

Explanation:

We are given that the current owner claims that over the past 5 years, the average daily revenue was $675 with a standard deviation of $75.

A sample of 30 days reveals a daily average revenue of $625.

Let
`\mu` = daily average revenue.

So, Null Hypothesis,
`H_0` :
`\mu` = $675 {means that the daily average revenue was $675}

Alternate Hypothesis,
`H_A` :
`\mu`
`\\eq` $675 {means that the daily average revenue was different from $675}

The test statistics that would be used here One-sample z test statistics as we know about the population standard deviation;

T.S. =
`(\bar X-\mu)/((\sigma)/(√(n) ) )` ~ N(0,1)

where,
`\bar X` = sample daily average revenue = $625

`\sigma` = population standard deviation = $75

n = sample of days = 30

Since, we are given that we have decided not to reject the null hypothesis which leads us to the conclusion that the daily average revenue was actually $675.