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. 68 women 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.) Part (a) State the null hypothesis H0: μ < 80 Part (b) State the alternative hypothesis. Ha: μ280
PART F PART i

Answer 1

The hypotheses are

Ha : μ>80

Given the sample size $n=68$ and sample mean
X 83
, sample standard deviation $s=10$

The test statistic is

X-80 83- 80 10 V68 t- 2.4738634

f) The P-value of the test is

P-value P(T> 2.4738634) P-value 0.0080

When $\alpha =0.05$ ,

Reject the null hypothesis since

P-value 0.0080 a 0.05

The conclusion is "There is sufficient evidence to conclude that the average number of hours women work each week is more than 80 hours".

i) The two sided confidence interval for mean based on the sample data is

-a) 10090

$\overline{x}\pm t_{1-\alpha /2,n-1}\frac{s}{\sqrt{n}}$

Here the 95% confidence interval is

10 83 ± t1-0.05/2,67 V68 (80.58,85.42)