Question

Consider the hypotheses shown below. Given that x overbarequals41​, sigmaequals13​, nequals36​, alphaequals0.10​, complete parts a and b. Upper H 0​: muless than or equals39 Upper H 1​: mugreater than39 ​a) What conclusion should be​ drawn? ​b) Determine the​ p-value for this test. ​

a) The​ z-test statistic is .92 . . ​(Round to two decimal places as​ needed.) The critical​ z-score(s) is(are) ?

fail to reject or reject and why

p value?

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is ,

H₀ :   = 39

H_a : > 39

Test statistic = z

= ( - ) / / n

= (41 - 39) / 13 / 36

= 0.92

= 0.10

Z _0.10 = 1.28

Critical value = 1.28

Test statistic < critical value

Fail to reject the null hypothesis .

P(z > 0.92) = 1 - P(z < 0.92) = 1 - 0.8212 = 0.1788