Question

Consider the following hypothesis test: Ho : μ = 130 Ha : μ 130 A sample of 55 is used. Identify the p-value and state your conclusion for each of the following sample results. Use a 0.01. Round the value of the test statistic to three decimal places. If required enter negative values as negative numbers. a. x 134 and s = 13 t-value p-value Select your answer conclusion l-select your answer- b. 125 and s 10 t-value Select your answer conclusionSelect your answer - Ho c. = 132 and s = 12.5 t-value p-value -Select your answer- conclusionSelect your answer ▼ Ho

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :  $\mu$ = 130

H_a : $\mu$   $\neq$ 130

n = 55

df = 54

(a)

Test statistic = t

= ($\bar x$ - $\mu$ ) / s / $\sqrt$ n

= (134 - 130) / 13 / $\sqrt$ 55

= 2.282

Test statistic = 2.282

P-value = 0.0265

$\alpha$ = 0.01

P-value > $\alpha$

Fail to reject the null hypothesis .

(b)

Test statistic = t

= ($\bar x$ - $\mu$ ) / s / $\sqrt$ n

= (125 - 130) / 10 / $\sqrt$ 55

= -3.708

Test statistic = -3.708

P-value = 0.0005

$\alpha$ = 0.01

P-value < $\alpha$

Reject the null hypothesis .

(c)

Test statistic = t

= ($\bar x$ - $\mu$ ) / s / $\sqrt$ n

= (132 - 130) / 12.5 / $\sqrt$ 55

= 1.187

Test statistic = 1.187

P-value = 0.2404

$\alpha$ = 0.01

P-value > $\alpha$

Fail to reject the null hypothesis .