Question

An accountant claims to be able to complete a standard tax return in under an hour. For a random sample of 24 tax returns, the accountant averaged 63.2 minutes. Assume that the population standard deviation is equal to 7.7 minutes and the population is normally distributed. What is the test statistic for the hypothesis test to check accountant's claim

Answer 1

Answer:

The test statistic for the hypothesis test to check accountant's claim is 2.036.

Step-by-step explanation:

We are given that an accountant claims to be able to complete a standard tax return in under an hour. For a random sample of 24 tax returns, the accountant averaged 63.2 minutes.

Assume that the population standard deviation is equal to 7.7 minutes and the population is normally distributed.

Let $\mu$ = average time to complete a standard tax return.

So, Null Hypothesis, $H_0$ : $\mu$ = 60 minutes   {means that an accountant can complete a standard tax return in an hour}

Alternate Hypothesis, $H_A$ : $\mu$ < 60 minutes   {means that an accountant can complete a standard tax return in under an hour}

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

                                  T.S.  = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$  ~ N(0,1)

where, $\bar X$ = sample average time = 63.2 minutes

            $\sigma$ = population standard deviation = 7.7 minutes

            n = sample of tax returns = 24

So, test statistics  =  $\frac{63.2-60}{\frac{7.7}{\sqrt{24} } }$

                               =  2.036

Hence, The value of test statistics for the hypothesis test to check accountant's claim is 2.036.