Question

Consider the hypotheses shown below. Given that x overbarequals113​, sigmaequals27​, nequals46​, alphaequals0.01​, complete parts a and b. Upper H 0​: muequals120 Upper H 1​: munot equals120

a) The​ z-test statistic is?

(Round to two decimal places as​ needed.)

b)The critical​ z-score(s) is(are) ?

(Round to two decimal places as​ needed.)

C)Reject or fail to reject, why or why not?

D)p-value?

(Round to four decimal places as​ needed.)

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :   = 120

H_a :    120

Test statistic = z

= ( - ) / / n

= (113 - 120) / 27 / 46

= -1.76

P(z < -1.76) = 0.0392

P-value = 0.0784

= 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z _0.005 = 2.576

Critical value = -2.576 or +2.576

Test statistic < critical value

Fail to reject the null hypothesis .