3..A private agency claims that the crash course it offers significantly increas

Question

3..A private agency claims that the crash course it offers significantly increases the writing scores of secretaries. The following gives the scores of eight secretaries before and after they attend the course.

         Before: 81, 75, 89, 91, 65, 70, 90, 64

         After:    97, 72, 93, 110, 78, 69, 115, 72

3.1)Determine whether the agent’s claim is correct at 0.05 significance level.

3.2)Find and interpret a 95% confidence interval for the mean writing score difference.

3.3)Find and interpret a 95% lower confidence limit for the mean score difference.

3.4) Interpret the difference between 3.1) and 3.3). What do you find?

Explanation / Answer

from above:

here tstat =d/std error =10.125/3.4869 =2.9037

for above t stat ; p value=0.01

as p value is less then 0.05 level, we reject null hypothesis.

and sufficient evidence to accept the claim that the crash course it offers significantly increases the writing scores of secretaries.

3.2) from above mean writing score difference:

sample mean =10.125

for 95% CI, t=2.3646

hence confidence interval =mean +/- t*std error =3.2588 ; 16.9912

which shows that before and after difference is significant

3.3)

for mean score difference

here degree of freedom =(S12/n1 +s22/n2)2/((s12/n1)2/(n1-1) +(s22/n2)2/(n2-1) ) =11

and std error =(S12/n1 +s22/n2)1/2 =7.5265

for 11 degree of freedom ; at 95% CI, t=2.201

hence confidence interval =(X2-X1|) +/- t*std error =-9.6907 ; 23.4411

which shows that before and after difference is not significant as it contain 0 as probable value.

3.4) 3.1 ) shows that  crash course offered significantly increases the writing scores of secretaries. but 3.3) shows that course offered does not increase scores significantly

before after difference(d) 81 97 16 75 72 -3 89 93 4 91 110 19 65 78 13 70 69 -1 90 115 25 64 72 8 mean 10.125 std deviaition 9.8624 std error= std dev/(n)^(1/2) 3.4869

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