Respuesta :
Answer:
Yes, it appear that the mean work week has increased for women at the 5% level.
Step-by-step explanation:
We are given that in 1955, Life Magazine reported that a 25-year-old mother of three worked, on average, an 80 hour week.
Suppose a study was done to determine if the mean work week has increased. 75 women were surveyed with the following results. The sample mean was 83; the sample standard deviation was 10.
Let [tex]\mu[/tex] = population mean work week for women
SO, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] [tex]\leq[/tex] 80 hour week {means that the mean work week has not increased for women}
Alternate Hypothesis, [tex]H_a[/tex] : [tex]\mu[/tex] > 80 hour week {means that the mean work week has increased for women}
The test statistics that will be used here is One-sample t test statistics because we don't know about population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean work week = 83
s = sample standard deviation = 10
n = sample of women = 75
So, test statistics = [tex]\frac{83-80}{\frac{10}{\sqrt{75} } }[/tex] ~ [tex]t_7_4[/tex]
= 2.598
Now, at 5% level of significance the t table gives critical value of 1.668 at 74 degree of freedom for one-tail test. Since our test statistics is more than the critical value of t as 2.598 > 1.668, so we have sufficient evidence to reject our null hypothesis as the test statistics will fall in the rejection region.
Therefore, we conclude that the mean work week has increased for women at the 5% level.
