The average (mean) length of workweeks (in hours) of 15 randomly selected employ
ID: 3242504 • Letter: T
Question
The average (mean) length of workweeks (in hours) of 15 randomly selected employees in the mining industry and 10 randomly selected employees in the manufacturing industry were obtained. Assuming both distribution are Normal, test the hypothesis that the two industries have the same mean length of workweek using = 0.10. The sample mean from the mining industry was 47.5 and the sample standard deviation was 5.5, the sample mean for the manufacturing industry was 43.5 and the sample standard deviation was 5.7.
Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: 1 = 2
Alternative hypothesis: 1 2
Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the difference between sample means is too big or if it is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.10. Using sample data, we will conduct a two-sample t-test of the null hypothesis.
Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).
SE = sqrt[(s12/n1) + (s22/n2)]
SE = 2.295
DF = 23
t = [ (x1 - x2) - d ] / SE
t = 1.743
where s1 is the standard deviation of sample 1, s2 is the standard deviation of sample 2, n1 is the size of sample 1, n2 is the size of sample 2, x1 is the mean of sample 1, x2 is the mean of sample 2, d is the hypothesized difference between the population means, and SE is the standard error.
Since we have a two-tailed test, the P-value is the probability that a t statistic having 23 degrees of freedom is more extreme than -1.743; that is, less than -1.743 or greater than 1.743
Thus, the P-value = 0.095
Interpret results. Since the P-value (0.095) is less than the significance level (0.10), we cannot accept the null hypothesis.
From the above test we do not have sufficient evidence in the favor of the claim that that the two industries have the same mean length of workweek.
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