Question

(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:

Answer 1

Answer:

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 $\mu$ = population mean.

So, Null Hypothesis, $H_0$ : $\mu$ = 100      {means that the population mean is equal to 100}  

Alternate Hypothesis, $H_A$ : $\mu$ > 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.  =  $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$  ~  $t_n_-_1$

where, $\bar X$ = sample mean = 98  

            s = sample standard deviation = 20

             n = sample size = 400

So, the test statistics =  $\frac{98-100}{\frac{20}{\sqrt{400} } }$   ~  $t_3_9_9$

                                     =  -2  

The value of t-test statistics is -2.

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

                 P($t_3_9_9$ < -2) = 0.0234   {using the t-table}