Question

A national firm reports mean earnings of

$70 ± $9

(μ ± σ) per unit sold over the lifetime of the company. A competing company over the past 16 reporting periods had reported mean earnings equal to $73 per unit sold. Conduct a one-sample z-test to determine whether mean earnings (in dollars per unit) are larger (compared to that reported by the national firm) at a 0.05 level of significance.

(a) State the value of the test statistic. (Round your answer to two decimal places.)
z =  

State whether to retain or reject the null hypothesis.

Retain the null hypothesis.Reject the null hypothesis.    

(b) Compute effect size using Cohen's d. (Round your answer to two decimal places.)
d =

Answer 1

SOLUTION:

From given data,

A national firm reports mean earnings of $70 ± $9 (μ ± σ) per unit sold over the lifetime of the company. A competing company over the past 16 reporting periods had reported mean earnings equal to $73 per unit sold. Conduct a one-sample z-test to determine whether mean earnings (in dollars per unit) are larger (compared to that reported by the national firm) at a 0.05 level of significance.

Where,

n = 16

= 70

= 9

= 73

significance level = 0.05

(a) State the value of the test statistic. (Round your answer to two decimal places.)

Test hypothesis:

Null hypothesis : : = 70

Alternative  hypothesis : : > 70

Right tailed test

The test statistic is,

Z = ( - ) / ( / sqrt(n))

Z = (73 - 70) / (9 / sqrt(16))

Z = 3 / 2.25

Z = 1.33

P-Value :

P-value = P(Z > 1.33)

P-value = 1 - P(Z<1.33)

P-value = 1 - 0.90824

P-value = 0.09176

We know that , significance level = = 0.05

Where,

P-value = 0.09176 > significance level = = 0.05

Then, We fail to reject null hypothesis ,so, retain null hypothesis .

Hence there is no evidence to accept the chain that the mean earnings are larger.

(b) Compute effect size using Cohen's d. (Round your answer to two decimal places.)

Effect size = d = ( - ) /

Effect size = d = (73 - 70) / 9

Effect size = d = 3 / 9

Effect size = d = 0.33