Question

Consider the following hypothesis test: H 0: = 17 H a: 17 A sample of 40 provided a sample mean of 14.13. The population standard deviation is 4. a. Compute the value of the test statistic (to 2 decimals). (If answer is negative, use minus "-" sign.) b. What is the p-value (to 4 decimals)? c. Using = .05, can it be concluded that the population mean is not equal to 17? Answer the next three questions using the critical value approach. d. Using = .05, what are the critical values for the test statistic (to 2 decimals)? ± e. State the rejection

Answer 1

Answer:

(a)  Test statistics = -4.54

(b) P-value = 1.9999

(c) We conclude that the population mean is equal to 17.

(d) Critical values for the test statistic are -1.96 and 1.96 .

(e) Test statistics is less than -1.96 or more than 1.96 represent the rejection region.

Step-by-step explanation:

We are given that ;

            Null Hypothesis, $H_0$ : $\mu$ = 17    where, $\mu$ = population mean

   Alternate Hypothesis, $H_1$ : $\mu \neq$ 17

Also, a sample of 40 provided a sample mean of 14.13 and the population standard deviation is 4 i.e.;

$Xbar$ = 14.13      $\sigma$ = 4    and   n = 40

(a) The test statistics used here will be;

        $\frac{Xbar - \mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

 Test statistics = $\frac{14.13 - 17}{\frac{4}{\sqrt{40} } }$ = -4.54

(b) P-value = P(Z > -4.54) = P(Z < 4.54) = 1 - P(Z >= 4.54)

From seeing the z % table we observe that the p-value will be less than 0.99995 in one -tail but in two tail case it will be less than 1.9999 .

(c) At 5% level of significance, we will accept null hypothesis because p -value is more than the significance level so we conclude that population mean is equal to 17.

(d) Using significance level of 5%, the critical values for the test statistic are -1.96 and 1.96 .

(e) If our test statistics is less than -1.96 or more than 1.96, then it will lie in the rejection region and we reject null hypothesis.

And since our test statistics is less than -1.96, so we reject $H_0$ and conclude that population mean is not equal to 17.