Question

3.  The data shows that for those 1,605 persons aged 27 years, the average number of hours worked in the prior week was 39.71 with a standard deviation of 10.16 hours. While for those 1,668 persons aged 49 years, average hours worked was 42.25 hours with a standard deviation of 10.58 hours.  Using the p-value approach and the 10% significance level, test the hypothesis that average hours worked by those aged 27 and 49 years are the same.

Answer 1

Answer Date: 21/05/2018 To test the hypothesis is that the hypothesis that average hours worked by those aged 27 and 49 years are the different at 10% significance level. The null and alternative hypothesisis, The t-test statistics is, By using MINITAB, find t-test statistics with the help of the following steps: 1) Import the data. 2) Select the Stat and choose the Basic Statistics option. 3) Select the 2 sample t and enter Summarized data. 4)Select Assume equal variances 5) Click option button choose Confidence level, Test difference and alternative hypothesis 6) Click Ok.

Two-Sample T-Test and ClI Sample Mean StDev SE Mean 1605 39.7 10.2 0.25 1668 42.3 10.6 0.26 Difference-mu (1) - mu (2) Estimate for difference: -2.54000 90% CI for difference : (-3.13693,-1.94307) 3271 Both use Pooled StDev 10.3762 From the MINITAB output, thet-test statistics is-7.00 The p-value for this test is, From the MINITAB output, thep-value for this test is l0.0001 Decision The conclusion is that p-value in this context is less than 0.10 which is 0.0001, so the null hypothesis is rejected at 10% level of significance. There is sufficient evidence to indicate that the hypothesis that average hours worked by those aged 27 and 49 years are the different. The result is statistically significant.