question archive A company sent seven of its employees to attend a course in a building self-confidence
A company sent seven of its employees to attend a course in a building self-confidence
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A company sent seven of its employees to attend a course in a building self-confidence. These employees were evaluated for their self-confidence before and after attending this course. The following table gives the scores (on a scale of 1 to 15, 1 being the lowest and 15 being the highest score) of these employees before and after they attended the course.
Before 8 5 4 9 6 9 5
After 10 8 5 11 6 7 9
a. Construct a 95% confidence interval for the mean μd of the pop- ulation of paired differences, where a paired difference is equal to the score of an employee before attending the course minus the score of the same employee after attending the course.
b. Test at a 1% significance level whether attending this course increases the mean score of employees.
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Ans:
| Before | After | d | |
| 1 | 8 | 10 | -2 |
| 2 | 5 | 8 | -3 |
| 3 | 4 | 5 | -1 |
| 4 | 9 | 11 | -2 |
| 5 | 6 | 6 | 0 |
| 6 | 9 | 7 | 2 |
| 7 | 5 | 9 | -4 |
| mean(d)= | -1.429 | ||
| sd= | 1.988 |
df=7-1=6
a)critical t value=tinv(0.05,6)=2.447
95% confidence interval for mean difference
=-1.429+/-2.447*(1.988/sqrt(7))
=-1.429+/-1.839
=(-3.267, 0.410)
b)
test statistic:
t=(-1.429-0)/(1.988/sqrt(7))
t=-1.901
p-value=tdist(1.901,6,1)=0.0530
As,p-value>0.01,we fail to reject the null hypothesis.
There is not sufficient evidence to conclude that attending this course increases the mean score of employees.
