Question

Wage and unions. Listed below are sample characteristics from a 1987 survey that examines average hourly wage rates for union and non-union workers. Nonunion: ?̅?? = 11.47; ???= 1206; ???= 6.58 Union: ?̅? = 12.19; ??= 376; ?? = 4.77

a. What is the difference in average hourly wages between union and nonunion workers?

b. Construct a 95% confidence interval around this difference.

c. Test the null hypothesis that there is no difference in wages across the two groups.

Answer 1

i am using minitab to solve the problem.

i am denoting the sample of union workers by 1 and the sample of non union workers by 2

steps:-

stat basic statistics 2 sample t select summarized data in sample 1, type 376 in sample size,12.19 in sample mean, 4.77 in standard deviation and in sample 2, type 1206 in sample size,11.47 in sample mean,6.58 in standard deviation   options in confidence level type 95 ,in hypothesized difference type 0, in alternative hypothesis select difference > hypothesized difference okok

your minitab output be:-

Two-Sample T-Test and CI

Method

μ₁: mean of Sample 1

µ₂: mean of Sample 2

Difference: μ₁ - µ₂

Equal variances are not assumed for this analysis.

Descriptive Statistics

Sample	N	Mean	StDev	SE Mean
Sample 1	376	12.19	4.77	0.25
Sample 2	1206	11.47	6.58	0.19

Estimation for Difference

Difference	95% CI for Difference
0.720	(0.111, 1.329)

Test

Null hypothesis	H₀: μ₁ - µ₂ = 0
Alternative hypothesis	H₁: μ₁ - µ₂ ≠ 0

T-Value	DF	P-Value
2.32	857	0.021

solution to the problem:-

a). the difference in average hourly wages between union and nonunion workers = 0.72

b). a 95% confidence interval around this difference be:   (0.111 , 1.329 )

c).hypothesis:-

	H₀: μ₁ - µ₂ = 0
	H₁: μ₁ - µ₂ ≠ 0

decision:-

based on p value:-

p value = 0.021 <0.05(alpha).

so, we reject the null hypothesis.

based on confidence interval :-

the hypothesized difference is not contained in the confidence interval, so we reject the null hypothesis.

conclusion:-

there is not sufficient evidence to support the claim that there is no difference in wages across the two groups at 0.05 level of significance.

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