Question

In $1955$, Life Magazine reported that the $25$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. $81$women were surveyed with the following results. The sample mean was$83$the sample

standard deviation was ten. Does it appear that the mean work week has increased for women at the role="math" localid="1650381098713" $5\%$level?

Short answer

Yes, the average work hours for women have $5\%$grown.

Step-by-step solution

 Given Information

$Let\mu =populationmeanworkweekforwomen$

So, Null Hypothesis , $H_0$: $\mu$$\le 80$hour week

( the mean work week has not increased for women )

Alternate Hypothesis , $H_0:\mu >80$

( the mean work week has increased for women )

Explanation

The test statistics that will be used here is One-sample t test statistics because we do not know about population standard deviation ;

$T.S=\frac{\overline{X}-\mu }{{\displaystyle \frac{s}{\sqrt{n}}}}~t=n-1$

Where,

$\overline{X}=samplemeanworkweek=83$

$s$ = sample standard deviation $=10$

$n$= sample of women $=75$

$So,t=\frac{83-80}{{\displaystyle \frac{10}{\sqrt{75}}}}~t=74$

$=2.598$