Question

In: Statistics and Probability

Exercise 10-3 A sample of 35 observations is selected from a normal population. The sample mean...

Exercise 10-3

A sample of 35 observations is selected from a normal population. The sample mean is 26, and the population standard deviation is 4. Conduct the following test of hypothesis using the .05 significance level.

  
H0 : μ ≤ 25
H1 : μ > 25
(a) Is this a one- or two-tailed test?
"Two-tailed"-the alternate hypothesis is different from direction.
"One-tailed"-the alternate hypothesis is greater than direction.
(b) What is the decision rule? (Round your answer to 2 decimal places.)
  (Click to select)Do not rejectReject H0,when z >
(c) What is the value of the test statistic? (Round your answer to 2 decimal places.)
  Value of the test statistic   
(d) What is your decision regarding H0?
Do not reject
Reject
There is (Click to select)sufficientinsufficient evidence to conclude that the population mean is greater than 25.
(e) What is the p-value? (Round your answer to 4 decimal places.)
  p-value     

Solutions

Expert Solution

Solution :

Given that,

Population mean = = 25

Sample mean = = 26

Population standard deviation = = 4

Sample size = n = 35

Level of significance = = 0.05

a)

This is a right tailed test.

"One-tailed"-the alternate hypothesis is greater than direction.

b)

Critical value ,

Zc = 1.64

Reject Ho if z > Zc

The test statistics,

Z =( - )/ (/n)

= ( 26 - 25 ) / 4/ 35)

= 1.48

The value of test statastic is 1.48

d)

Snice, It is observe that , z = 1.48 < Zc = 1.64 , It is concluded that do not reject null hypothesis.

Therefore , sufficient evidence to conclude that the population mean is greater than 25.

e)

p-value = 1 - P(Z < z)

= 1 - 0.9306

= 0.0694


Related Solutions

A sample of 35 observations is selected from a normal population. The sample mean is 26,...
A sample of 35 observations is selected from a normal population. The sample mean is 26, and the population standard deviation is 4. Conduct the following test of hypothesis using the 0.05 significance level. H0: μ ≤ 25 H1: μ > 25 Is this a one- or two-tailed test? "One-tailed"—the alternate hypothesis is greater than direction. "Two-tailed"—the alternate hypothesis is different from direction. What is the decision rule? (Round your answer to 2 decimal places.) What is the value of...
A sample of 36 observations is selected from a normal population. The sample mean is 21,...
A sample of 36 observations is selected from a normal population. The sample mean is 21, and the population standard deviation is 5. Conduct the following test of hypothesis using the 0.05 significance level. H0: μ ≤ 20 H1: μ > 20 a). What is the decision rule? (Round your answer to 2 decimal places.) b). What is the value of the test statistic? (Round your answer to 2 decimal places.) c). What is the p-value? (Round your answer to...
A sample of 31 observations is selected from a normal population. The sample mean is 23,...
A sample of 31 observations is selected from a normal population. The sample mean is 23, and the population standard deviation is 2. Conduct the following test of hypothesis using the 0.10 significance level. H0: μ ≤ 22 H1: μ > 22 Is this a one- or two-tailed test? One-tailed test Two-tailed test What is the decision rule? Reject H0 when z > 1.282 Reject H0 when z ≤ 1.282 What is the value of the test statistic? (Round your...
A sample of 37 observations is selected from a normal population. The sample mean is 21,...
A sample of 37 observations is selected from a normal population. The sample mean is 21, and the population standard deviation is 3. Conduct the following test of hypothesis using the 0.02 significance level. H0: μ ≤ 20 H1: μ > 20 Is this a one- or two-tailed test? One-tailed test Two-tailed test What is the decision rule? Reject H0 when z > 2.054 Reject H0 when z ≤ 2.054 What is the value of the test statistic? (Round your...
A sample of 39 observations is selected from a normal population. The sample mean is 28,...
A sample of 39 observations is selected from a normal population. The sample mean is 28, and the population standard deviation is 4. Conduct the following test of hypothesis using the .05 significance level.    H0 : μ ≤ 26 H1 : μ > 26 (a) Is this a one- or two-tailed test? "Two-tailed"-the alternate hypothesis is different from direction. "One-tailed"-the alternate hypothesis is greater than direction. (b) What is the decision rule? (Round your answer to 2 decimal places.)...
A sample of 44 observations is selected from a normal population. The sample mean is 46,...
A sample of 44 observations is selected from a normal population. The sample mean is 46, and the population standard deviation is 7. Conduct the following test of hypothesis using the 0.01 significance level. H0: μ = 50 H1: μ ≠ 50 Is this a one- or two-tailed test? One-tailed test Two-tailed test What is the decision rule? Reject H0 if −2.576 < z < 2.576 Reject H0 if z < −2.576 or z > 2.576 What is the value...
A sample of 50 observations is selected from a normal population. The sample mean is 47,...
A sample of 50 observations is selected from a normal population. The sample mean is 47, and the population standard deviation is 7. Conduct the following test of hypothesis using the 0.10 significance level: H0: μ = 48 H1: μ ≠ 48 a. Is this a one- or two-tailed test? (Click to select)  Two-tailed test  One-tailed test b. What is the decision rule? Reject H0 and accept H1 when z does not lie in the region from  to. c. What is the value...
A sample of 33 observations is selected from a normal population. The sample mean is 53,...
A sample of 33 observations is selected from a normal population. The sample mean is 53, and the population standard deviation is 6. Conduct the following test of hypothesis using the 0.05 significance level. H0: μ = 57 H1: μ ≠ 57 What is the decision rule? Reject H0 if −1.960 < z < 1.960 Reject H0 if z < −1.960 or z > 1.960 What is the value of the test statistic? (Negative amount should be indicated by a...
A sample of 60 observations is selected from a normal population. The sample mean is 37,...
A sample of 60 observations is selected from a normal population. The sample mean is 37, and the population standard deviation is 8. Conduct the following test of hypothesis using the 0.10 significance level. H0 : μ ≤ 36 H1 : μ > 36 1. What is the decision rule? (Round the final answer to 3 decimal places.) H1 when z> 2. What is the value of the test statistic? (Round the final answer to 2 decimal places.) 3. What...
A sample of 31 observations is selected from a normal population. The sample mean is 69,...
A sample of 31 observations is selected from a normal population. The sample mean is 69, and the population standard deviation is 8. Conduct the following test of hypothesis using the 0.01 significance level. H0: μ = 72 H1: μ ≠ 72 Is this a one- or two-tailed test? One-tailed test Two-tailed test What is the decision rule? Reject H0 if −2.576 < z < 2.576 Reject H0 if z < −2.576 or z > 2.576 What is the value...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT