Solution to Last year the employees of the city health department donated an average of $ 8 … - Sikademy
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Mirian Woke

Last year the employees of the city health department donated an average of $ 8 to the rescue squad. Test the hypothesis at the 0.01 level of significance that the average contribution this year is still $ 8 if a random sample of 35 employees showed an average donation of $ 8.90 with a standard deviation of $ 1.75.

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The following null and alternative hypotheses need to be tested:



This corresponds to a two-tailed test, for which a t-test for one mean, with unknown population standard deviation, using the sample standard deviation, will be used.

Based on the information provided, the significance level is \alpha = 0.01, df=n-1=34 degrees of freedom, and the critical value for a two-tailed test is t_c=2.728394.

The rejection region for this two-tailed test is R = \{t: |t| > 2.728394\}.

The t-statistic is computed as follows:


Since it is observed that |t| = 3.042555 > 2.728394=t_c , it is then concluded that the null hypothesis is rejected.

Using the P-value approach:

The p-value for two-tailed, df=34 degrees of freedom, t=3.042555, is p=0.0045, and since p=0.0045<0.01=\alpha, it is concluded that the null hypothesis is rejected.

Therefore, there is enough evidence to claim that the population mean \mu is different than 8, at the \alpha = 0.01 significance level.

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