Question

In the book Business Research Methods, Donald R. Cooper and C. William Emory (1995) discuss a manager who wishes to compare the effectiveness of two methods for training new salespeople. The authors describe the situation as follows:

The company selects 22 sales trainees who are randomly divided into two equal experimental groups—one receives type A and the other type B training. The salespeople are then assigned and managed without regard to the training they have received. At the year’s end, the manager reviews the performances of salespeople in these groups and finds the following results:

	A Group	B Group
Average Weekly Sales	x⎯⎯1x¯1 = $1,350	x⎯⎯2x¯2 = $1,086
Standard Deviation	s1 = 233	s2 = 263

(a) Set up the null and alternative hypotheses needed to attempt to establish that type A training results in higher mean weekly sales than does type B training.

H₀: µ_A ? µ_B ?  versus H_a: µ_A ? µ_B  >

(b) Because different sales trainees are assigned to the two experimental groups, it is reasonable to believe that the two samples are independent. Assuming that the normality assumption holds, and using the equal variances procedure, test the hypotheses you set up in part a at level of significance .10, .05, .01 and .001. How much evidence is there that type A training produces results that are superior to those of type B? (Round your answer to 3 decimal places.)

t =

(Click to select)RejectDo not reject H0 with ? equal to .10.

(Click to select)Do not rejectReject H0 with ? equal to .05

(Click to select)Do not rejectReject H0 with ? equal to .01

(Click to select)Do not rejectReject H0 with ? equal to .001

(Click to select)WeakVery strongNoStrongExtremely strong  evidence that µA ? µ B > 0

(c) Use the equal variances procedure to calculate a 95 percent confidence interval for the difference between the mean weekly sales obtained when type A training is used and the mean weekly sales obtained when type B training is used. Interpret this interval. (Round your answer to 2 decimal places.)

Confidence interval [, ]

Answer 1

: Average performances of salespeople with Type A training

: Average performances of salespeople with Type B training

Claim : Type A training results in higher mean weekly sales than does type B training i.e

(a) Set up the null and alternative hypotheses needed to attempt to establish that type A training results in higher mean weekly sales than does type B training.

Right tailed test

(b)

t = 2.492

Degrees of freedom = 19

For right tailed test,

for 19 degrees of freedom, P(t > 2.492) =0.011

For =0.10 ; As P-Value is less than Level of significance i.e (P-value:0.0111 < 0.1:Level of significance); Reject Null Hypothesis

For = 0.05 ; As P-Value is less than Level of significance i.e (P-value:0.0111 < 0.05:Level of significance); Reject Null Hypothesis

For = 0.01 ; As P-Value is less than Level of significance i.e (P-value:0.0111 > 0.01:Level of significance); Fail to Reject Null Hypothesis

For = 0.001 ; As P-Value is less than Level of significance i.e (P-value:0.0111 > 0.001:Level of significance); Fail to Reject Null Hypothesis

No Strong evidence that µ_A - µ _B > 0

(c) Use the equal variances procedure to calculate a 95 percent confidence interval for the difference between the mean weekly sales obtained when type A training is used and the mean weekly sales obtained when type B training is used

95 percent confidence interval for the difference between two mean

for 95% confidence level = (100-95)/100 = 0.05

/2 = 0.05/2 = 0.025

95 percent confidence interval for the difference between the mean weekly sales obtained when type A training is used and the mean weekly sales obtained when type B training is used

Confidence interval [42.3, 485.7]

At 95% confidence level , the difference between the mean weekly sales obtained when type A training is used and the mean weekly sales obtained when type B training is used is between 42.3 and 485.7