PLEASE SHOW ALL WORK Here are the IQ test scores of 31 seven

PLEASE SHOW ALL WORK.

Here are the IQ test scores of 31 seventh-grade girls in a Midwest school district. These 31 girls are an SRS of all seventh-grade girls in the school district. Suppose that the standard deviation of IQ scores in this population is known to be sigma = 16. We expect the distribution of IQ scores to be close to Normal. Make a stemplot of the distribution of these 31 scores (split the stems) to verify that there are no major departures from Normality. You have now checked the \"simple conditions\" to the extent possible. (Enter your answers from smallest to largest. Enter NONE in any unused answer blanks.) Estimate the mean IQ score for all seventh-grade girls in the school district, using a 99% confidence interval. (Round your answers to two decimal places.)

Solution

a)

Ordering the data,

70
73
85
88
91
92
95
99
100
102
103
103
103
104
105
108
108
111
111
111
112
113
114
114
114
115
118
123
129
130
132

Thus, the stem leaf plot is

b)

Getting the mean and standard deviation,

X = 105.6774194
s = 14.69327986

Note that              
              
Lower Bound = X - z(alpha/2) * s / sqrt(n)              
Upper Bound = X + z(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.005          
X = sample mean =    105.6774194          
z(alpha/2) = critical z for the confidence interval =    2.575829304          
s = sample standard deviation =    14.69327986          
n = sample size =    31          
              
Thus,              
              
Lower bound =    98.87982914          
Upper bound =    112.4750097          
              
Thus, the confidence interval is              
              
(   98.87982914   ,   112.4750097 ) [ANSWER]

Stem	Leaves
7	7 3
8	5 8
9	1 2 5 9
10	0 2 3 3 3 4 5 8 8
11	1 1 1 2 3 4 4 4 5 8
12	3 9
13	0 2