Question

Consider the hypotheses below. Ho : μ-50 H1 : μ # 50 Given that X-55, s-20, n-20, and α-0.01, answer the questions below a. What conclusion should be drawn? b. Use technology to determine the p-value for this test. a. Detemine the critical value(s). The critical value(s) is(are) (Round to three decimal places as needed. Use a comma to separate answers as needed.)

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :  $\mu$ = 50

H_a : $\mu$   $\neq$ 50

$\alpha$ = 0.01

$\alpha$ / 2 = 0.01 /2 = 0.005

t_0.005,19 = +/-2.861

Critical values are : -2.861 , +2.861

Test statistic = t

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

= (55 - 50) / 20 / $\sqrt$ 20

= 1.12

Test statistic < critical value

Reject the null hypothesis .

n = 20

df = 19

P-value = 0.2767