Question

Let's Consider the Following Hypothesis

Ho: µ ≤ 25

Ha: µ > 25

1. Is this Hypothesis:

Lower tail, Upper tail, or two tail?

2. What is the Critical Value with α = 0.01?

3. A sample of 40 provided a sample mean of 26.4. The population standard deviation is 6. Then the test Statistic is what

4. What is the P-value =?

5. Do we reject ho, do not reject ho, or neither

Answer 1

Solution:

1)

Upper tailed.

2)

Critical value of  the significance level is α = 0.01, and the critical value for a upper-tailed test is

= 2.33

3)

The test statistics,

Z =( - )/ (/n)

= (26.4 - 25 ) / ( 6 / 40 )

= 1.48

4)

P-value = P(Z > z )

= 1 - P(Z < 1.48)

= 1 - 0.9306

= 0.0694

5)

The p-value is p = 0.0694, and since p = 0.0694 > 0.01, it is concluded do not reject Ho.