13. \"Sunlight makes everyone feel better.\" To test this claim, 30 college stud

Question

13. "Sunlight makes everyone feel better." To test this claim, 30 college students receive special lights for their bedrooms that slowly turn on in the morning with imitation sunlight. The experiment takes place in January, when t is still dark out in the morning. Prior to participation, the students fill out a questionnaire to measure their general mood. The average score was 2.73. After three wecks with the special light they fill in the questionnaire again. The average score this time was 3.13. The sample standard deviation of the differences was 0.822. (a) What is the value of the standard error for the difference in average mood score? b) Calculate a 95% confidence interval for the difference in average mood scores after before Interpret your interval calculated above

Explanation / Answer

a) std error =s/(n)1/2 =0.822/(30)1/2 =0.1501

b)averaage difference =3.13-2.73 =0.4

therefore 95% confidence interval =0.145 to 0.655

c) above interval gives 95% confidence to contain true mean increase in general mood increase after implementing imitating sunlight

for 90% CI; and 29 degree of freedom, value of t= 1.6991 margin of error E=t*std error                            = 0.255 lower confidence bound=sample mean-margin of error = 0.145 Upper confidence bound=sample mean+margin of error= 0.655

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