1. The average hourly wage of a sample of 150 workers is plant A was Rs. 2.56 with a S.D of Rs.1.08. The average wage of a sample of 200 workers in plant B was Rs. 2.87 with a S.D of Rs.1.28. Can an applicant safety assume that the hourly wages paid by plant B are greater than those paid by plant A?
Answers
Answer:
To compare means:
Null hypothesis: means are the same; alternative hypothesis: means differ.
0: 1 = 2; : 1 ≠ 2
Let the significance level = 0.1
Rejection region: ≤ −1.645; ≥ 1.645
Compute z-score:
=
¯1 − ¯2
√
1
2
1
+
2
2
2
=
2.56 − 2.87
√
1
2
150 +
1.2
2
200
= −2.633
As z-score lies in the rejection region, we reject null hypothesis. Thus, at 0.1 significance level,
there is sufficient evidence to reject the claim that the means are equal (null hypothesis).
To compare standard deviations:
Null hypothesis: standard deviations are equal; alternative hypothesis: standard deviations differ.
0: 1
2 = 2
2
; : 1
2 ≠ 2
2
Let the significance level = 0.1
Test score: = (
1
2
)
2
= 0.6944
Since the first sample had the smaller standard deviation, this is a left-tailed test.
F-distribution has two degrees of freedom, 150-1=149 and 200-1=199.
The p-value is p=Fcdf(0,0.6944,149,199) = 0.0096, which is less than our significance level.
Thus, we should reject the null hypothesis that standard deviations are equal.
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