A sample of 76 female workers and another sample of 48 male workers from a state produced mean weekly earnings of $743.50 for the females and $777.63 for the males. Suppose that the population standard deviations of the weekly earnings are $80.05 for the females and $88.68 for the males. The null hypothesis is that the mean weekly earnings are the same for females and males, while the alternative hypothesis is that the mean weekly earnings for females is less than the mean weekly earnings for males. Directions: • Label your answers with the correct statistical symbols. • If you use the Ti, identify which function and values you used to calculate. If you solve by hand, show all steps. 2.1. Derive the corresponding 95% confidence interval, rounded to two decimal places, for the difference between the mean weekly earnings for all female and male workers in this state. 2.2. What is the point estimate? 2.3. What is E?
A sample of 76 female workers and another sample of 48 male workers from a state produced
2.1. Derive the corresponding 95% confidence interval, rounded to two decimal places, for the difference between the mean weekly earnings for all female and male workers in this state.
2.2. What is the point estimate?
2.3. What is E?
2.5. The significance level for the test is 1%. What is/are the critical value(s)?
26. What is the value of the test statistic, rounded to three decimal places?
2.7. What is the p-value for this test, rounded to four decimal places?
2. 8. Using the p-value approach, do you reject or fail to reject the null hypothesis at the 1% significance level? Explain your decision.
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