A university investigation was conducted to determine whether women and men complete medical school in significantly different amounts of time, on the average. Two independent random samples were selected and the following summary information concerning times to completion of medical school computed:

Women Men
Sample size 90 100
Sample mean 8.4 years 8.5 years
Sample std 0.6 year 0.5 years

Required:
Perform the appropriate test to see if there is a significant difference in time to completion of medical school between women and men.

[tex]Null \ H_{yp}: \mu_{men} = \mu_{women}\\\\Alt \ Hyp: \mu_{men} \neq \mu_{women}\\\\Std\ Error\ (SE) = \sqrt{(\frac{s_1^2}{n_1}) + (\frac{s_2^2}{n_2})} \\\\[/tex]

[tex]= \sqrt{(\frac{0.62}{90}) + (\frac{0.52}{100})} \\\\= 0.08[/tex]

[tex]test\ statistic \ t = \frac{(x_1 - x_2)}{SE} = \frac{(8.4 - 8.5)}{0.08} = -1.25[/tex]

Degrees of freedom

[tex]= \frac{(\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2})^2}{\frac{(\frac{s_1^2}{n_1})^2}{(n_1 - 1)}} + \frac{(\frac{s_2^2}{n_2)^2}}{(n_2 - 1)} \\\\= 174[/tex]

Considering a degree of 5% importance

T for df critical value = 174 and sig level = 0.05 is +1.973

Let area of refusal shall be t < -1.973 or t > +1.973

Because statistical tests weren't in the refusal zone, they may not deny that zero but find that perhaps the argument how both women and men undergo med school is considerably different lengths of time is not significantly supported.