Question

2. A sample of 636 male workers were asked how many hours they worked in the previous week, the mean was 45.5 with a standard deviation of 15.16. Does this suggest that the population mean work week for men exceeds 40 hours? To answer:

a. State the assumptions in this question

b. State the null and alternative hypotheses.

c. Calculate the t-statistic and also report the p-value

d. Make a conclusion based on a significance level of 0.05.

Answer 1

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Answer:

a)

It is assumed the it is a normal distribution as per central lmit theorm

In the given situation, the random variable is defined as the number of working hours of male workers in previous week, X, and the parameter is the population mean working hours of male workers for previous week, µ.

b)

Set the null and alternative hypotheses for the given situation as below.

(The sample does not provide enough evidence to claim that the mean working hours of male workers in the previous week exceeds 40 hours.

Versus

(The sample provides enough evidence to claim that the mean working hours of male workers in the previous week exceeds 40 hours.

c)

It is given that the t-statistics for testing the null hypothesis about mean is obtained as

The sample size is given as so the test statistics follows t-distribution with degrees of freedom.

From part (b), the stated alternative hypothesis indicates a one-tailed test.

So, define the P-value of test statistics as below.

Use the Excel command, to find the above defined P-value.

Thus, the resultant P-value is approximately 0.0000.

Therefore, approximately with probability of 0.0000, the male workers of the sample are likely to work more than 40 hours.

d)

As the P-value is less than level of significance, so, there is strong evidence to reject the null hypothesis.

Hence, the sample data provides strong evidence to conclude that the mean working hours of male workers in the previous week will exceeds 40 hours at 1% level of significance.