UESTION 8 The charitable f wealthy individuals; the average annual donor income
ID: 3316736 • Letter: U
Question
UESTION 8 The charitable f wealthy individuals; the average annual donor income in the most recent survey was right at $100,000. The foundation believes the average has now increased. A for a large metropolitan hospital is conducting a study to characterize its donor base. In the past, most donations have come from relatively random sample of 200 current donors showed a mean annual income of $103,157 and a standard deviation of $27,498 (A) Specity a hypothesis test to test the foundation's claim (B ompared to the most recent survey, test your hypothesis at the 10% level by show your sample mean, standard erro, degrees of (C) Report the p-vale for this test D) Report on whether we accept or reject the null freedom and test statistic. For the toolbar, press ALT F10 (PC) or ALT-FN+F10 (Mac) ately strong rejection, or a so-so rejection?Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: < 100,000
Alternative hypothesis: > 100,000
Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the sample mean is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.10. The test method is a one-sample t-test.
Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).
SE = s / sqrt(n)
S.E = 1944.4
DF = n - 1
D.F = 199
t = (x - ) / SE
t = 1.62
where s is the standard deviation of the sample, x is the sample mean, is the hypothesized population mean, and n is the sample size.
The observed sample mean produced a t statistic test statistic of 1.62.
Thus the P-value in this analysis is 0.0526
Interpret results. Since the P-value (0.0526) is smaller than the significance level (0.10), we have to reject the null hypothesis.
Reject the null hypothesis, From the above test we have strong evidence in the favor of the claim that averages has increased.
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