Consider the following hypothesis test: H0: 20 Ha: < 20 A sample of 50 provided

Question

Consider the following hypothesis test:

H0:   20

Ha:  < 20

A sample of 50 provided a sample mean of 19.5. The population standard deviation is 1.6.

a. Compute the value of the test statistic (to 2 decimals).

b. What is the p-value (to 3 decimals)?

c. Using  = .05, can it be concluded that the population mean is less than 20? - Select your answer -YesNoItem 3

d. Using  = .05, what is the critical value for the test statistic?

e. State the rejection rule: Reject H0 if z is - Select your answer -greater than or equal togreater thanless than or equal toless thanequal tonot equal toItem 5 the critical value.

f. Using  = .05, can it be concluded that the population mean is less than 20? - Select your answer -YesNoItem 6

Explanation / Answer

Given:-

sample mean is X¯=19.5,

population standard deviation is =1.6,

sample size is n = 50

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: =20

Ha: <20

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

(2) Rejection Region

The significance level is =0.05, and the critical value for a left-tailed test is zc=1.64.

The rejection region for this left-tailed test is R={z:z<1.64}

(3) Test Statistics

The z-statistic is computed as follows:

z = [ (X¯0) / (/n) ] = [ (19.520) / (1.6/50) ] = 2.21

(4) Decision about the null hypothesis

Since it is observed that z=2.21<zc=1.64, it is then concluded that the null hypothesis is rejected.

P-value : The p-value is p = 0.0136

since p = 0.0136 < 0.05, it is concluded that the null hypothesis is rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population mean is less than 20, at the 0.05 significance level.

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.