54 Alice Chang and her colleagues (A. Chang, L. Rosenthal. R. H. Bryant, R. H. R

Question

54 Alice Chang and her colleagues (A. Chang, L. Rosenthal. R. H. Bryant, R. H. Rosenthal, R. M. Heidlage, and B. K. Fritzler. "Comparing High School and College Students' Leisure In- terests and Stress Ratings," Behavioral Research Therapy 31(2), 1993) tested 559 high school students using a leisure-interest checklist (LIC) survey. The means and standard deviations for each of the seven LIC factor scales are given in the following table for n 252 male students and n 307 female students a Give a 95% confidence interval for the difference in the means for male and female stu- dents for the cultural activity scale. Interpret this interval.

Explanation / Answer

Solution:

We are given n = 252 for male and n = 307 for female

The confidence interval formula is given as below:

Confidence interval = (X1bar – X2bar) -/+ t*[(S1^2/N1)+(S2^2/N2)]

Where, t is the critical value.

Part a

Here, we have to find 95% confidence interval for difference in the means for male and female for cultural activity.

We are given

X1bar = 11.48

X2bar = 13.21

S1 = 5.69

S2 = 5.31

N1 = 252

N2 = 307

Degrees of freedom = 252 + 307 – 2 = 557

Confidence level = 95%

Critical t value = 1.9642

Confidence interval = (11.48 – 13.21) -/+ 1.9642*sqrt[(5.69^2/252)+(5.31^2/307)]

Confidence interval = -1.73 -/+ 0.921962

Lower limit = -1.73 - 0.921962 = -2.65196

Upper limit = -1.73 + 0.921962 = -0.80804

Confidence interval = (-2.65196, -0.80804)

Part b

Here, we have to find the 90% confidence interval for difference in means for social fun.

We are given

X1bar = 22.05

X2bar = 25.96

S1 = 5.12

S2 = 5.07

N1 = 252

N2 = 307

Degrees of freedom = 252 + 307 – 2 = 557

Confidence level = 90%

Critical t value = 1.6476

Confidence interval = (22.05 – 25.96) -/+ 1.6476*sqrt[(5.12^2/252)+(5.07^2/307)]

Confidence interval = -3.91 -/+ 0.713916

Lower limit = -3.91 - 0.713916 = -4.62392

Upper limit = -3.91 + 0.713916 = -3.19608

Confidence interval = (-4.62392, -3.19608)

Part c

Yes, means for males and females for the two LIC activities appeared to differ because the value 0 does not lies within this interval.

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