Question

Assume that z is the test statistic.

(a) H_o: μ = 22.5, H_a: μ > 22.5; x = 25.5, σ = 5.2, n = 23
(i) Calculate the test statistic z. (Give your answer correct to two decimal places.)


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


(b) H_o: μ = 200, H_a: μ < 200; x = 192.4, σ = 39, n = 32
(i) Calculate the test statistic z. (Give your answer correct to two decimal places.)


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


(c) H_o: μ = 12.4, H_a: μ  12.4; x = 11.4, σ = 5, n = 20
(i) Calculate the test statistic z. (Give your answer correct to two decimal places.)


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

Answer 1

Solution :

a) Given that

= 22.5

=25.5

=5.2

n = 23

This is the right tailed test .

The null and alternative hypothesis is ,

H0 :   = 22.5

Ha : > 22.5

Test statistic = z

= ( - ) / / n

= (25.5- 22.5 ) / 5.2 / 23

= 2.77

Test statistic = z = 2.77

P(z > 2.77 ) = 1 - P(z < 2.77 ) = 1 -0.9972  

P-value =0.0028

b) Given that

= 200

=192.4

= 39

n = 32

This is the left tailed test .

The null and alternative hypothesis is ,

H0 :   = 200

Ha : < 200

Test statistic = z

= ( - ) / / n

= (192.4- 200 ) / 39 / 32

= -1.10

Test statistic = z = -1.10

P-value =0.1357

c) Given that

= 12.4

=11.4

=5

n = 20

This is the two tailed test .

The null and alternative hypothesis is ,

H0 :   = 12.4

Ha : 12.4

Test statistic = z

= ( - ) / / n

= (11.4- 12.4 ) / 5 / 20

= -0.89

Test statistic = z =-0.89

P(z < -0.89 ) = 0.1867

P-value = 2 * 0.1867 = 0.3734