6. Testing a population mean-Reaching a conclusion by the critical value approac

Question

6. Testing a population mean-Reaching a conclusion by the critical value approach Aa Aa You conduct a hypothesis test of a population mean at a significance level of -01 using a sample of size n-83. The population standard deviation is unknown, so you use the t-test statistic. Your test statistic follows a t distribution with n 1- 82 degrees of freedom when the null hypothesis is true as an equality, and its value obtained from the sample is t-2.55 Use the Distributions tool to help you answer the questions that follow. Select a DistributionY Distributions If you perform a lower tall test, the critical value for your test statistic is: (Hint: The value you enter should be a negative number and include the minus sign.) You the null hypothesis in this case, because the test statistic is: O Greater than the critical value-t O Less than the critical value-t If you perform a two-tailed test, the lower and upper critical values for your test statistic are: -to/2 and to/2 You the null hypothesis in this case, because the test statistic is: O Greater than the critical value-to/ O Less than the critical value -ta O In between the critical values-to/n and ta/z Session

Explanation / Answer

Solution:-

a)

The critical value for the one-tailed test is

tcritical = - 2.37

We reject the null hypothesis in this case, because the test statistics is less than the critical value - talpha.

b)

The critical value for the two-tailed test is

tcritical = + 2.64

Rejection region is - 2.64 > t > 2.64

We retain the null hypothesis in this case, because the test statistics is between the critical values talpha/2 and - talpha/2..

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