Question

1. To test H0: o=40 versus H1: o< 40​, a random sample of sizen=29 is obtained from a population that is known to be normally distributed.

​a.  If the sample standard deviation is determined to be s=36.2, compute the test statistic.

​b. If the researcher decides to test this hypothesis at the a= 0.10 level of​ significance, use technology to determine the​ P-value.

c. Will the researcher reject the null​ hypothesis?

2.To test H0: o=4.9 versus H1: o ≠ 4.9, a random sample of size n=19 is obtained from a population that is known to be normally distributed.

​(a) If the sample standard deviation is determined to be s=6.1, compute the test statistic.

​(b) If the researcher decides to test this hypothesis at the a=0.05 level of​ significance, use technology to determine the​ P-value.

​(c) Will the researcher reject the null​ hypothesis?

Answer 1

(1)

(a)

H0: Null Hypothesis: = 40

H1: Alternative Hypothesis: < 40

n = 29

s = 36.2

Test Statistic is given by:

(b)

df = 29 - 1 = 28

By Technology, P - value = 0.2636

(c)

Since P - value = 0.2636 is greater than = 0.10, the difference is not significant.

The researcher will fail to reject the null​ hypothesis.

(2)

(a)

H0: Null Hypothesis: = 4.9

H1: Alternative Hypothesis: 4.9

n = 19

s = 6.1

Test Statistic is given by:

(b)

df = 19 - 1 = 18

By Technology, P - value = 0.0637

(c)

Since P - value = 0.0637 is greater than = 0.05, the difference is not significant.

The researcher will fail to reject the null​ hypothesis.