Question

Minitab printout

One-Sample T: weight of cats

Descriptive Statistics (weight is in pounds)

N Mean StDev SE Mean 95% CI for μ
33 9.300 1.707 0.297 (8.694, 9.905) μ: mean of weight of cats Test Null hypothesis H₀: μ = 8.5
Alternative hypothesis H₁: μ ≠ 8.5
T-Value P-Value
2.69 0.011

a. Looking at the confidence interval estimate, write a confidence statement for the mean weight for all cats.
b. State your decision for the null hypothesis and show how you arrived at it.
c. Write your conclusion.
d. Can we safely say that the mean weight of all cats will be at least 8 pounds? Please give a reason for your answer.

Answer 1

Solution:

Given:

Minitab printout
One-Sample T: weight of cats
Descriptive Statistics (weight is in pounds)
N	Mean	StDev	SE Mean	95% CI for µ
33	9.3	1.707	0.297	(8.694 , 9.905 )
μ: mean of weight of cats Test Null hypothesis H₀: μ = 8.5
Alternative hypothesis H₁: μ ≠ 8.5
T-Value	P-value
2.69	0.011

Part a. Looking at the confidence interval estimate, write a confidence statement for the mean weight for all cats.

From given output 95% confidence interval is: ( 8.694 , 9.905)

Thus we are 95% confident that the true mean weight for all cats is between 8.694 pounds to 9.905 pounds.

Part b. State your decision for the null hypothesis and show how you arrived at it.

from given output, we have T-value = 2.69 and P-value = 0.011

Decision Rule: Reject null hypothesis H0, when P-value < 0.05 level of significance, otherwise we fail to reject H0.

Since P-value = 0.011 < 0.05 level of significance, we reject null hypothesis H0.

Part c. Write your conclusion.

Since we have rejected null hypothesis H₀: μ = 8.5, we conclude that the mean weight for all cats is different from 8.5 pounds.

Part d. Can we safely say that the mean weight of all cats will be at least 8 pounds? Please give a reason for your answer.

Since we have 95% confidence interval of mean weight for all cats which  is between 8.694 pounds to 9.905 pounds which exceeds 8 pounds. Thus we can safely say that the mean weight of all cats will be at least 8 pounds