The president of a consulting firm is considering discounting one of its require

Question

The president of a consulting firm is considering discounting one of its required training programs for the employees. A comitee decided that if the proportion of employees who think the training program is worth continuing is less than 0.4, then the training program will be discountinued. To test if the proportion of employees who think the training program is worth continuing is less than 0.4. We conduct the hypothesis

H0: P0.4

Ha: P<0.4

where p is the proportion of employees who think the training program is worth continuing. A sample of 125 employeess is drawn and 45 employees said that they think the training program is worth continuing. Use a 0.01 level of significance to answer the following questions.

A.) Compute the sample proportion

B.)Compute the test statistic

C.) Compute the critical value

D.)What is your conclusion based on the critical value?

Please show work.

Explanation / Answer

a) sample proportion = 45/125 = 0.36

b)

Test statistic:

= sqrt[ P * ( 1 - P ) / n ]

= sqrt [(0.4 * 0.6) / 125]

= 0.04

z = (p - P) /

= (.36 - .4)/0.04

= -1

c) With alpha = .01 the critical z score is -2.33. We reject Ho if z < -2.33.

d) As z value is greater than critical value so we fail to reject the null hypothesis.

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