Question

The mean height of a random sample of 47 students who take part in athletic activities at NRDC is 175cm with a standard deviation of 5cm while a random sample of 132 students who showed no interest in athletics had a mean of 170cm and a standard deviation of 7cm. (a) Construct a 99% confidence interval for the difference in the mean heights of the two groups of students. (b) Are students who take part in athletic activities taller? Test at the 1% level of significance

Answer 1

(a)

Confidence interval for the difference in means is given as:

$Upper\ limit = \bar{X_1}-\bar{X_2}+Margin\ of\ error$

$Lower\ limit = \bar{X_1}-\bar{X_2}-Margin\ of\ error$

$Margin\ of\ error = t_{\alpha/2,df}*SE$

SE is given by by :

SE = 0.9504

$t_{\alpha/2,df} = t_{0.01/2,113.242} = t_{0.005,113.242} = 2.62$

$Margin\ of\ error = t_{\alpha/2,df}*SE = 2.62*0.9504 = 2.49$

99% confidence interval for the difference in the mean heights of the two groups of students :

$Upper\ limit = 175-170+2.49 = 5+2.49 = 7.49$

$Lower\ limit = 175-170-2.49 = 5-2.49 = 2.51$

b)

We conduct T-test for two Means :

Hence, we conclude that Students who take part in athletic activities are actually taller at 1% level of significance.