Question

Suppose you have a sample of 33 women who exercise daily, and who have an average duration of labor of 16.9 hours and a sample variance of 20.3 hours. You want to test the hypothesis that women who exercise daily have a different duration of labor than all women.

Calculate the t statistic.

Answer 1

Answer:

$\displaystyle{\mathbf{\frac{16.9 - \mu_0}{0.7842}}}$

Step-by-step explanation:

For computing the t statistic it is essential to first state the hypothesis. Suppose the average duration of labour for women is $\mu_0$. Using the t statistic will help us determine whether our sample mean is sufficiently high or low in order to make a conclusion that women who exercise daily have a different duration of labor than all women.

let

$H_0 \colon \mu = \mu_0$

Here we will use the fact that for a random sample drawn from any population,

$\frac{\bar{x} - \mu_0}{s/\sqrt{n}} \sim t_{n-1}$

where,

• $\bar{x}$ = sample mean = 16.9
• $\mu_0$ = our assumed mean as mentioned above
• $n$ = size of the sample = 33
• s = sample standard deviation = $\sqrt{20.3} = 4.505$

Plugging in the numerical values, we get

$= \displaystyle{\frac{16.9 - \mu_0}{0.7842}}$ is the required t statistic.