Question

In light of a recent large corporation bankruptcy, auditors are becoming increasingly concerned about the possibility of fraud. Auditors might be helped in determining the chances of fraud if they carefully measure cash flow. To evaluate this possibility, samples of midlevel auditors from CPA firms were presented with cash-flow information from a fraud case, and they were asked to indicate the chance of material fraud on a scale from 0 to 100. A random sample of 41 auditors used the cashflow information. Their mean assessment was 37.3, and the sample standard deviation was 22. For an independent random sample of 41 auditors not using the cash-flow information, the sample mean and standard deviation were, respectively, 49.9 and 27. Assuming that the two population distributions are normal with equal variances, a. test at significance level 5%, against a two-sided alternative, the null hypothesis that the population means are equal; b. find the p-value of the test above.

          In light of a recent large corporation bankruptcy, auditors are
becoming increasingly concerned about the possibility of fraud.
Auditors might be helped in determining the chances of fraud if
they carefully measure cash flow. To evaluate this possibility,
samples of midlevel auditors from CPA firms were presented with
cash-flow information from a fraud case, and they were asked to
indicate the chance of material fraud on a scale from 0 to 100. A
random sample of 41 auditors used the cashflow information. Their
mean assessment was 37.3, and the sample standard deviation was 22.
For an independent random sample of 41 auditors not using the
cash-flow information, the sample mean and standard deviation were,
respectively, 49.9 and 27. Assuming that the two population
distributions are normal with equal variances, a. test at
significance level 5%, against a two-sided alternative, the null
hypothesis that the population means are equal; b. find the p-value
of the test above.

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Added by Jimmy W.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Ajiboye Tunde

02/03/2022

Step 1

The null hypothesis (H0) is that the population means are equal, i.e., μ1 = μ2. The alternative hypothesis (H1) is that the population means are not equal, i.e., μ1 ≠ μ2. We can use a two-sample t-test to test these hypotheses. The test statistic is calculated as Show more…

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In light of a recent large corporation bankruptcy, auditors are becoming increasingly concerned about the possibility of fraud. Auditors might be helped in determining the chances of fraud if they carefully measure cash flow. To evaluate this possibility, samples of midlevel auditors from CPA firms were presented with cash-flow information from a fraud case, and they were asked to indicate the chance of material fraud on a scale from 0 to 100. A random sample of 41 auditors used the cashflow information. Their mean assessment was 37.3, and the sample standard deviation was 22. For an independent random sample of 41 auditors not using the cash-flow information, the sample mean and standard deviation were, respectively, 49.9 and 27. Assuming that the two population distributions are normal with equal variances, a. test at significance level 5%, against a two-sided alternative, the null hypothesis that the population means are equal; b. find the p-value of the test above.

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Transcript

00:01 In light of a recent large corporation bankruptcy, auditors are becoming increasingly concerned about the possibility of fraud.

00:07 Auditors might be helped in determine the chance of fraud if they are carefully, if they carefully measure cash flow.

00:13 To evaluate this possibility, samples of mid -level auditors from cpa firms were presented with cash flow information from a fraud case and they were asked to indicate the chance of a material fraud on a scale of 0 to 100.

00:25 A random sample of 41 auditors used to cash flow information.

00:29 Their mean assessment was 37 .3 and the sample standard division was 22 for an independent random sample of 41 auditors not using the cash flow information the sample mean and the sample side division we have respectively were 49 .9 and 27 assuming that the two population distributions are normal with equal variances our question is is that we should perform a test at 5 percent level of significance against a two -sided alternative they did not hypothesis and the alternative hypothesis that the population means are actually equal and the question b says we should get the value of our p value so let's go into worksheet and extract out all of the necessary details so the auditors that use the cash flow information i can decide to represent that with sample one and no cash flow information i can decide to represent that with sample so so let's extract our details so a random sample of 41 auditors used the cash flow information.

01:36 So that means our n1 is equals to 41.

01:39 And from this n1, we're able to realize that the mean assessment was 37 .3 and the standard division was 22.

01:46 So x1 bar is equal to 37 .3 and the sample standardization was equals to 22.

01:55 For the no cash flow, we have a sample of 41 auditors.

02:03 So our n2 is equals to 41 and we're so that the sample means 49 .9.

02:10 So that means our x2 bar is because to 49 .9 and our sample standard deviation, the second sample station that gives us 27...

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