Solution to 1. For a sample of 35 items from a population for which the standard deviation … - Sikademy
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1. For a sample of 35 items from a population for which the standard deviation is σ= 20.5 , the sample mean is 458.0. At the 0.05 level of significance, test H0: μ= 450 versus H1: μ> 450 . Determine and interpret the p-value for the test.

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The following null and alternative hypotheses need to be tested:



This corresponds to a right-tailed test, for which a z-test for one mean, with known population standard deviation will be used.

Based on the information provided, the significance level is \alpha = 0.05, and the critical value for a right-tailed test is z_c = 1.6449.

The rejection region for this right-tailed test is R = \{z: z > 1.6449\}.

The z-statistic is computed as follows:


Using the P-value approach:

The p-value is p=P(Z>2.308714)=0.010480, and since p=0.010480<0.05=\alpha, it is concluded that the null hypothesis is rejected.

Therefore, there is enough evidence to claim that the population mean \mu is greater than 450, at the \alpha = 0.05 significance level.

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Question ID: mtid-4-stid-46-sqid-1942-qpid-412