Question

Random sample of 20 men who six feet or taller is obtained. The incomes in thousands of dollar
are as follows:
10.8 12.7 13.9 18.1 19.4 21.3 23.5 24.0 24.6 25.0
25.4 27.7 30.1 30.6 32.3 33 .3 34.7 38.8 40.3 55.5
a) Test the hypothesis that the lower quartile of incomes for tall men is 24,500. α=0.05.

b) find a 90% confidence interval for the lower quartile?

Answer 1

a) Using the given value of lower quartile income covered into 24.5.

So using the one-sample t-test

The hypothesis is

H₀=sample mean is equal to the given population mean

H₁=sample mean is not equal to the given population mean.

Using the t-test test statistic is 1.1008 and the p-value is 0.284 which is greater than the level of significant 0.05. Hence we accept the null hypothesis sample mean is equal to the given population mean.

b) The 90% confidence interval for a lower quartile is (16.5 to 24.3).