Question

A randomly chosen group of eight students at Stanford University was given a test to measure their authoritarian attitude (on a 40 to 200 scale, with 200 being most authoritarian. The results were

Student 1 2 3 4 5 6 7 8

Score 111 76 98 102 128 96 101 55

a) Construct a 95% confidence interval for the mean authoritarian atti- tude score for this student body.

b) What assumption do you have to make for this to be a valid confidence interval?

c) Does the data show the violation of this assumption? (Hint: Obtain the histogram of the data)

Answer 1

A)
mean=   95.88    [Excel function used -> AVERAGE]
sd=   22.02    [Excel function used -> STDEV]  
n=   8.00    [Excel function used -> COUNT]
alpha=   5%  

CI = mean +- t(a/2,n-1)*(sd/sqrt(n))      
lower   = 95.875 - 2.365*(22.0223/sqrt(8)) = 77.46
upper   = 95.875 + 2.365*(22.0223/sqrt(8)) = 114.29

B)
here normal distribution is assumed.

c)

Row Labels	Count of DATA
50-64	1
65-79	1
95-109	4
110-124	1
125-139	1
Grand Total	8

the data follows normal distribution as graph is bell shaped. hence above assumtpion is not violated