Question

| A sample of 100 is used and the population standard deviation is 15 Compute the p-value and state your conclusion for each of the following sa ple esults use -0.01. Round z value to two decimal places and p-value to four decimal places. If your answer is zero, enter "O". Enter negative value as negative number. MacBook Air

Answer 1

z- value is given by the formula

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

here $\fn_cm \mu$ = 81, $\fn_cm \sigma$ = 15 and n= 100

And null and alternative hypothesis are:

H_o : $\dpi{80} \fn_cm \mu \geq 81$

H₁ :$\dpi{80} \fn_cm \mu< 81$ (left tail test)

a. $\dpi{80} \fn_cm \bar{x} = 80.5$

$\dpi{80} \fn_cm z = \frac{80.5 - 81}{15}$

= -0.033

From the table, the p-value is 0.4868

Since p-value > $\dpi{80} \fn_cm \alpha =0.01$

Conclusion: Do Not Reject H₀

b.  $\dpi{80} \fn_cm \bar{x} = 77.5$

$\dpi{80} \fn_cm z = \frac{77.5 - 81}{15}$

= -0.233

From the table, the p-value is 0.4079

Since p-value > $\dpi{80} \fn_cm \alpha =0.01$

Conclusion: Do Not Reject H₀

c. $\dpi{80} \fn_cm \bar{x} = 75.5$

$\dpi{80} \fn_cm z = \frac{75.5 - 81}{15}$

= -0.3667

From the table, the p-value is 0.3572

Since p-value > $\dpi{80} \fn_cm \alpha =0.01$

Conclusion: Do Not Reject H₀

d. $\dpi{80} \fn_cm \bar{x} = 83$

$\dpi{80} \fn_cm z = \frac{83 - 81}{15}$

= 0.1333

From the table, the p-value is 0..4470

Since p-value > $\dpi{80} \fn_cm \alpha =0.01$

Conclusion: Do Not Reject H₀