Question

Assume that z is the test statistic. (Give your answers correct to two decimal places.)

(a) Calculate the value of z for Ho: μ = 10, σ = 3.3, n = 37, x = 11.1.

(b) Calculate the value of z for Ho: μ = 120, σ = 22, n = 25, x = 127.

(c) Calculate the value of z for Ho: μ = 18.2, σ = 4.3, n = 145, x = 19.05.

(d) Calculate the value of z for Ho: μ = 81, σ = 12.7, n = 55, x = 80.2.

You may need to use the appropriate table in Appendix B to answer this question.

Answer 1

Solution :

Given that ,

(a)

$\bar x$ = 11.1

$\mu$ = 10

$\sigma$ = 3.3

n = 37

Test statistic = z

= ( $\bar x$ - $\mu$ ) / $\sigma$ / $\sqrt$ n

= (11.1 - 10) / 3.3 / $\sqrt$ 37

= 2.02

Test statistic = 2.02

(b)

$\bar x$ = 127

$\mu$ = 120

$\sigma$ = 22

n = 25

Test statistic = z

= ( $\bar x$ - $\mu$ ) / $\sigma$ / $\sqrt$ n

= (127 - 120) / 22 / $\sqrt$ 25

= 1.59

Test statistic = 1.59

(c)

$\bar x$ = 19.05

$\mu$ = 18.2

$\sigma$ = 4.3

n = 145

Test statistic = z

= ( $\bar x$ - $\mu$ ) / $\sigma$ / $\sqrt$ n

= (19.05 - 18.2) / 4.3 / $\sqrt$ 145

= 2.38

Test statistic = 2.38

(d)

$\bar x$ = 80.2

$\mu$ = 81

$\sigma$ = 12.7

n = 55

Test statistic = z

= ( $\bar x$ - $\mu$ ) / $\sigma$ / $\sqrt$ n

= (80.2 - 81) / 12.7 / $\sqrt$ 55

= -0.46

Test statistic = -0.46