Use the following information in problems 1 through 9 to imp

Use the following information in problems 1 through 9 to implement a t minutes, it to . Seven manufacturing companies agreed ime-management program in hopes of improving productivity. The average times, in ok the companies to produce the same piece of equipment are listed below. Does this information indicate that the program CHANGED production time? Assume normal population distributions, you need a t test Assume a two-sided alternative. Use SPSS. Use =0.05. Company 1 2 3 4 56 7 Before program (1) 75 112 89 95 80 105 110 80 10510 Before progrann (1) I 75 112 | 89 95 After program (2) 70 110 88 100 80 100 99

Solution

Sorry I don\'t have SPSS.

I can done this problem by using MINITAB.

This is paired t-test.

Hypothesis for the test is,

H0 : µ_d = 0 Vs H1 : µ_d 0

given that test is two sided.

where µ_d is the population mean of difference.

The test statitstic is,

t = (Xbar - µ_d ) / (s/sqrt(n) )

n = number of pairs = 7

Xbar = mean of difference.

s = standard deviation of difference.

alpha = 0.05

MINITAB steps :

STAT --> Basic statistics --> Paired -t (test and confidence interval) --> samples in column --> first sample after program --> second sample before program --> options : confidence level = 0.95, Test mean = 0, Alternative = not equal --> ok

This will gives us following output.

Paired T-Test and CI: after, before

Paired T for after - before

N Mean StDev SE Mean
after 7 92.4286 13.8065 5.2184
before 7 95.1429 14.5766 5.5094
Difference 7 -2.71429 4.99047 1.88622

95% CI for mean difference: (-7.32970, 1.90113)
T-Test of mean difference = 0 (vs not = 0): T-Value = -1.44 P-Value = 0.200

The absolute value of T is 1.44

and P-value = 0.200

P-value > alpha

Accept H0 at 5% level of significance.

mean difference is 0.