Question

6. If we do not know σ=1.20 in the aforementioned problem 4, we will use a T-procedure to perform the hypothesis test. Below is the output: 1769821 1.288449 .117363 7.063763 53 6.390265 -2.3134 52 degrees of freedon a) What is the sample mean of the 53 observed values? (2 credits If we perform a two-tailed test, what conclusion we can make based on the p value in the table above. (4 credits) b) If we perform a one-tailed test, what conclusion we can make based on the p value in the table above. (4 credits) c)
no 6

Answer 1

(a)

Sample Mean = $\bar{x}$ = 6.590565

(b)

t score = - 2.3134

ndf =n - 1 = 53 - 1 = 52

Two Tail Test

By Technology, P - Value < 0.0001

Since P - value is less than $\alpha$ = 0.01, the difference is significant.Reject null hypothesis.

Conclusion:
The data support the claim that the population mean is different from 7.

(c)

t score = - 2.3134

ndf =n - 1 = 53 - 1 = 52

One Tail Left Side Test

By Technology, P - Value < 0.0001

Since P - value is less than $\alpha$ = 0.01, the difference is significant.Reject null hypothesis.

Conclusion:
The data support the claim that the population mean is less than - 7.