Question

The first time you measured the complaints made at your 4 stores, you found that they produced 12,15,10, and 9 complaints per day. You hired a consulting firm that promised to reduce the complaints. When they were done you remeasured and found the complaints were now 10,12,8, and 10, respectively. To determine if the results was statistically significant, you ran a test. Are you 95% sure they were successful?

a.Yes

b.Cannot tell

c.No

Answer 1

H₀ was accepted.So average before and after the training is same So they are not successful

Paired sample T-test test, using T distribution (DF=3) (two-tailed)

1. H₀ hypothesis
Since p-value > ?, H₀ was accepted.
The average of the Group 1's population is considered to be equal to the ?0
In other words, the difference between the average of the Group 1 and ?0 is not big enough to be statistically significant.

Hypotheses

H₀: ?_d = ?₀
H₁: ?_d ? ?₀i

Test statistic

2. P-value
p-value equals 0.181532, ( p(x?t) = 0.0907659 ). This means that if we would reject H₀, the chance of type I error (rejecting a correct H₀) would be too high: 0.1815 (18.15%)
The larger the p-value the more it supports H₀

3. The statistics
The test statistic t equals -1.732052, is in the 95% critical value accepted range: [-3.1816 : 3.1816]
x=-1.50, is in the 95% accepted range: [-2.7600 : 2.7600]


4. Effect size
The observed standardized effect size is large (0.87). That indicates that the magnitude of the difference between the average and ?0 is large