Question

Assume that z is the test statistic.

(a) H₀: μ = 22.5, H_a: μ > 22.5; x = 24.8, σ = 7.6, n = 40
(i) Calculate the test statistic z. (Round your answer to two decimal places.)


(ii) Calculate the p-value. (Round your answer to four decimal places.)


(b) H₀: μ = 200, H_a: μ < 200; x = 191.5, σ = 38, n = 30
(i) Calculate the test statistic z. (Round your answer to two decimal places.)


(ii) Calculate the p-value. (Round your answer to four decimal places.)


(c) H₀: μ = 12.4, H_a: μ ≠ 12.4; x = 10.9, σ = 4.2, n = 23
(i) Calculate the test statistic z. (Round your answer to two decimal places.)


(ii) Calculate the p-value. (Round your answer to four decimal places.)

Answer 1

Solution :

a) The null and alternative hypothesis is ,

H₀ :   = 22.5

H_a : > 22.5

= 24.8

= 7.6

n = 40

Test statistic = z

= ( - ) / / n

= (24.8 - 22.5) / 7.6 / 40

= 1.91

This is the right tailed test

p(Z > 1.91) = 1-P (Z < 1.91) = 1 - 0.9719

P-value = 0.0281

b) The null and alternative hypothesis is ,

H₀ :   = 200

H_a : <  200

= 191.5

= 38

n = 30

Test statistic = z

= ( - ) / / n

= (191.5 - 200) / 38 / 30

= -1.23

This is the left tailed test

p(Z < -1.23)

P-value = 0.1093

c) The null and alternative hypothesis is ,

H₀ :   = 12.4

H_a :     12.4

= 10.9

= 4.2

n = 23

Test statistic = z

= ( - ) / / n

= (10.9 - 12.4) / 4.2 / 23

= -1.71

This is the two tailed test

p(Z < -1.71) = 0.0436

P-value = 2 * p(Z < -1.71)

P-value = 2 * 0.0436

P-value = 0.0872