Question

Consider the following hypothesis test:

H0: m>=76

Ha: m<76

A sample of 140 is used and the population standard deviation is 12. Compute the p-value and state your conclusion for each of the following sample results. Use a=0.02. Round z-value to two decimal places and p-value to four decimal places. If your answer is zero, enter "0". Enter negative value as negative number.

a. x=73.5

z-value ________

p-value ________

Conclusion: (Reject/Do Not Reject) H0

b.

b. x=72.5

z-value ________

p-value ________

Conclusion: (Reject/Do Not Reject) H0

c. x=71

z-value ________

p-value ________

Conclusion: (Reject/Do Not Reject) H0

d. x=77.5

z-value ________

p-value ________

Conclusion: (Reject/Do Not Reject) H0

Answer 1

z- value is given by the formula

$\fn_cm z= \frac{x - \mu }{\sigma }$

here $\fn_cm \mu$ = 76, $\fn_cm \sigma$ = 12 and n= 140

a. x=73.5

$\dpi{80} \fn_cm z = \frac{73.5-76}{12}$

= -0.25

From the table, the p-value is .8026

Since p-value > $\dpi{80} \fn_cm \alpha =0.02$

Conclusion: Do Not Reject H₀

b. x=72.5

$\dpi{80} \fn_cm z = \frac{72.5-76}{12}$

= -0.29

From the table, the p-value is 0.7718

Since p-value > $\dpi{80} \fn_cm \alpha =0.02$

Conclusion: Do Not Reject H₀

c. x=71

$\dpi{80} \fn_cm z = \frac{71-76}{12}$

= -0.42

From the table, the p-value is 0.6745

Since p-value > $\dpi{80} \fn_cm \alpha =0.02$

Conclusion: Do Not Reject H₀

d. x=77.5

$\dpi{80} \fn_cm z = \frac{77-76}{12}$

= 0.08

From the table, the p-value is 0.9362

Since p-value > $\dpi{80} \fn_cm \alpha =0.02$

Conclusion: Do Not Reject H₀