Question

The mean of the population (µ) on a test that measures math skills of middle school students is 200. The variance  is 100. The test scores for the students in Mr. Petris’s class at Suburban Middle School are given below.

195        203        200               193        207               201        199               197        203               199       

195        220        200               202        200               193        205               187        218               189       

173        209        190               190        206               209        185               179        188               205

Use a rejection region with a statistical significance of 5% (p<.05) only in the upper tail.

1. What is the name of the z-test you will conduct?
2. What would be an appropriate null hypothesis that you could test using the provided information?
3. What should you conclude about the null hypothesis you developed (reject or fail to reject)? Explain.

Now use a rejection region with a total statistical significance of 5% (p<.05) incorporated in both the upper and lower tails.

4. What is the name of the z-test you will conduct?
5. What would be an appropriate null hypothesis that you could test using the provided information?
6. What should you conclude about the null hypothesis you developed (reject or fail to reject)? Explain.

Answer 1

Soln

1)

We will be using one tailed z test

Sample Mean (x) = 198

n = 30

Alpha = 0.05

Null and Alternate Hypothesis

H₀: µ = 200

H_a: µ > 200

Test Statistic

Z = (x - µ₀)/ σ/n^1/2 = (198 - 200)/ 10/30^1/2 = -1.10

P(X>198) = 1 – P(X<198) = 1 – P(z<-1.10) = 1 - 0.1357 = 0.8643

Result

Since the p-value is greater than 0.05, the data is not statistically significant and we fail to reject the null hypothesis

Rejection Region Method: Since the test statistic (-1.1) is less than 1.645, we fail to reject the null hypothesis

Conclusion

Mean math score is 200

2)

We will be using two tailed z test

Alpha = 0.05

Null and Alternate Hypothesis

H₀: µ = 200

H_a: µ <> 200

Test Statistic

Z = (x - µ₀)/ σ/n^1/2 = (198 - 200)/ 10/30^1/2 = -1.10

Result

Since the Z does not lie in the rejection region, we fail to reject the null hypothesis

Conclusion

Mean math score is 200