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

Answer:

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

Step-by-step 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, $H_A$ : $\mu$ $\neq$ $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. =  $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$  ~ 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.