Question

In 1955, Life Magazine reported that a 25-year-old mother of three worked, on average, an 80 hour week. Recently, many groups have been studying whether or not the women's movement has, in fact, resulted in an increase in the average work week for women (combining employment and at-home work). Suppose a study was done to determine if the mean work week has increased. 80women were surveyed with the following results. The sample mean was 83; the sample standard deviation was 10. Does it appear that the mean work week has increased for women at the 5% level?

Note: If you are using a Student's t-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)

1. What is the test statistic? (If using the z distribution round your answers to two decimal places, and if using the t distribution round your answers to three decimal places.)

2. What is the p-value?

p-value < 0.0100.010 < p-value < 0.050     0.050 < p-value < 0.100p-value > 0.100

Explain what the p-value means for this problem. If H₀  is false, then there is a chance equal to the p-value that the average number of hours women work each week is 83 hours. or more. If

H₀ is false, then there is a chance equal to the p-value that the average number of hours women work each week is not 83 hours or more.     If H₀ is true, then there is a chance equal to the p-value that the average number of hours women work each week is not 83 hours or more. If H₀ is true, then there is a chance equal to the p-value that the average number of hours women work each week is 83 hours or more.

3. Sketch a picture of this situation. Label and scale the horizontal axis and shade the region(s) corresponding to the p-value.

4. Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write an appropriate conclusion.

(i) Alpha (Enter an exact number as an integer, fraction, or decimal.)
α =  

(ii) Decision:

reject the null hypothesisdo not reject the null hypothesis     

(iii) Reason for decision:

Since α < p-value, we reject the null hypothesis.Since α > p-value, we do not reject the null hypothesis.     Since α < p-value, we do not reject the null hypothesis.Since α > p-value, we reject the null hypothesis.

(iv) Conclusion:

There is sufficient evidence to conclude that the average number of hours women work each week is more than 80 hours.There is not sufficient evidence to conclude that the average number of hours women work each week is more than 80 hours

4. Construct a 95% confidence interval for the true mean. Sketch the graph of the situation. Label the point estimate and the lower and upper bounds of the confidence interval. (Round your lower and upper bounds to two decimal places.)

Answer 1