Question

A sample of 31 observations is selected from a normal population. The sample mean is 11, and the population standard deviation is 3. Conduct the following test of hypothesis using the 0.05 significance level.

H₀: μ ≤ 10

H₁: μ > 10

1. Is this a one- or two-tailed test?

• One-tailed test

• Two-tailed test

2. What is the decision rule?

• Reject H₀ when z > 1.645

• Reject H₀ when z ≤ 1.645

3. What is the value of the test statistic? (Round your answer to 2 decimal places.)

4. What is your decision regarding H₀?

• Reject H₀

• Fail to reject H₀

1. e-1. What is the p-value? (Round your answer to 4 decimal places.)

1. e-2. Interpret the p-value? (Round your final answer to 2 decimal places.)

Answer 1

Solution:

a)
It is a one tail test.

b)
We Reject H0 when Z Score is Large. Therefore, We reject the H0 when Z > 1.645

c)

(X-μ)

X = 10 ;
u = 11
s = 3
n = 31,

Therefore,

Z = 1.86

d)
Z = 1.86 > 1.645 ; Hence, We reject the H0

P value for Z = 1.86 is,
p value = 0.0314

Since, P value is less than 0.05; We Reject the null hypothesis.

Hence, we conclude that the mean of the selected sample is less than 11.