Question

Consider the hypotheses shown below. Given that x overbar equals 53​, sigma equals13​, n equals 38​, alpha equals 0.01​, complete parts a and b. Upper H 0​: mu less than or equals 51 Upper H 1​: mugreater than 51 ​a) What conclusion should be​ drawn? ​b) Determine the​ p-value for this test.

​a) The​ z-test statistic is

b) the p- value

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is ,

H₀ :   = 51

H_a : > 51

(a)

Test statistic = z

= ( - ) / / n

= (53 - 51) / 13 / 38

= 0.95

(b)

P(z > 0.95) = 1 - P(z < 0.95) = 1 - 0.8289 = 0.1711

P-value = 0.1711