(20 points) A statistics practitioner calculated the mean and the standard deviation from a sample of 400. They are x = 98 and s = 20: (a) Compute the p-value in order to test H0 : = 100 against H1 : 6= 100: (b) Compute the p-value in order to test H0 : = 100 against H1 : > 100:

The P-value is 0.0234.

Step-by-step explanation:

We are given that a statistics practitioner calculated the mean and the standard deviation from a sample of 400. They are x = 98 and s = 20.

Let = population mean.

So, Null Hypothesis, : = 100      {means that the population mean is equal to 100}  

Alternate Hypothesis, : > 100     {means that the population mean is more than 100}

The test statistics that will be used here is One-sample t-test statistics because we don't know about population standard deviation;

                               T.S.  =    ~  

where, = sample mean = 98  

            s = sample standard deviation = 20

             n = sample size = 400

So, the test statistics =     ~  

                                     =  -2  

The value of t-test statistics is -2.

Now, the P-value of the test statistics is given by;

                 P( < -2) = 0.0234   {using the t-table}

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