Question

The Australian Bureau of Statistics (ABS) has collected data on the part-time employment patterns of full-time male students in Australia and found that they worked 16 hours per week on average. A researcher believes that female students may work fewer hours on average than male students. Accordingly, she selects 36 female students at random and finds the average number of hours worked per week to be 13.5 and the standard deviation is 7 hours. To see if her belief is substantiated, conduct the appropriate test at a significance level of 5% and interpret the result. State the assumptions made.

Answer 1

Right Tailed t test, Single Mean

Given: = 16 Hours, = 13.5 Hours, s = 7 Hours, n = 36, = 0.05

Assumptions:

(a) The selection of the sample is done by a simple random sampling.

(b) The population from which the sample has been taken is approximately normally distributed.

(c) The samples are independent of each other.

The Hypothesis:

H0: = 16: The average number of hours worked by women per week is equal to 16.

Ha: < 16: The average number of hours worked by women per week is lesser than 16. (Claim)

This is a Left tailed test

The Test Statistic: Since the population standard deviation is known, we still use the students t test.

The test statistic is given by the equation:

$t = \frac{\bar{x}-\mu }{\frac{s}{\sqrt{n}}} = \frac{13.5-16}{\frac{7}{\sqrt{36}}} = -2.143$

t observed = -2.143

The p Value: The p value (Left tailed) for t = -2.143, for degrees of freedom (df) = n-1 = 35, is; p value = 0.0196

The Critical Value: The critical value (Left Tail) at = 0.05, for df = 36, tcritical= -1.69

The Decision Rule:  

The Critical Value Method: If tobserved is < -tcritical.

The p-value Method: If P value is < , Then Reject H0.

The Decision:

The Critical Value Method: Since tobserved (-2.143) is < -t critical (-1.69), we Reject H0.

The p-value Method: Since P value (0.0196) is < (0.05) , We Reject H0.

The Conclusion: There is sufficient evidence at the 95% significance level to conclude that the average number of hours worked by women per week is lesser than 16.