Question

The average manufacturing work week in Chicago was 40.1 hours last year. The population standard deviation is believed to be 3.5. It is believed that the recession has led to a reduction in the average work week.

a) To test the validity of this belief, the hypotheses are

b) You interviewed 225 people and found that the average was 39.8 hours. What is the p-value?

c) What is your conclusion at α=0.05?

d) Use critical value approach to decide whether you should reject the null hypothesis.

Answer 1

Solution-A:

• Null Hypothesis: The population mean sales volume with new bonus plan is less than or equal to 14

Alternate Hypothesis: The population mean sales volume with new bonus plan is more than 14

Let mean sales volume =

If we fail to reject this null hypothesis, we can conclude that there is not sufficient evidence to reject the assumption that the population mean sales volume with new bonus plan is less than or equal to 14

Solution-B:

• Null Hypothesis: Recession has led to reduction in the average work week from 40.1 hours

Alternate Hypothesis: Recession has not led to reduction in the average work week from 40.1 hours

Let mean length woek week for population =

If we fail to reject this null hypothesis, we can conclude that there is not sufficient evidence to reject the belief that recession has led to reduction in the average work week from 40.1 hours

Solution-C:

• Null Hypothesis: Proportion of citizens supporting an increase in cigarette taxes is less than or equal to 0.66

Alternate Hypothesis: Proportion of citizens supporting an increase in cigarette taxes is more than 0.66

Let population proportion =

If we fail to reject this null hypothesis, we can conclude that there is not sufficient evidence to reject the assumption that proportion of citizens supporting an increase in cigarette taxes is less than or equal to 0.66