hello. how can i show the formula for question f in this problem. i need to know
ID: 3294632 • Letter: H
Question
hello. how can i show the formula for question f in this problem. i need to know how it should read in this problem?
95% confidence interval for u can be obtained by using the following formula. sample mean +/- t critical value*s/sqrt n
question i need an answer for below?
Determine the 95% confidence interval
for the population mean, based on the sample mean.
problem is below
Aresearcherhypothesizesthatindividualswho listen to classical music will score differently from the general population on a test of spatial ability. On a standardized test of spatial ability, m 5 58. A random sample of 14 individuals who listen to classical music is given the same test. Their scores on the test are 52, 59, 63, 65, 58, 55, 62, 63, 53, 59, 57, 61, 60, 59.
(Jackson 224)
Jackson, Sherri L. Research Methods and Statistics: A Critical Thinking Approach, 5th Edition. Cengage Learning, 20150101. VitalBook file.
The citation provided is a guideline. Please check each citation for accuracy before use.
Explanation / Answer
Solution
95% confidence interval = sample mean (Xbar) +/- t critical value*s/sqrt n, where
n = sample size (14),
s = sample standard deviation = sqrt of sample variance = [[1,n]{(xi – Xbar)2}]/(n - 1)
t critical value = upper 2.5% point of t-distribution with (n - 1) = (13) degrees of freedom. This can be read off from Standard t-distribution Table or by using Excel Function.[2.5% = (100 - 95)/2; division by 2 is because of +/- in CI]
Detailed calculations are shown below:
i
xi
(xi-Xbar)
(xi-Xbar)^2
1
52
-7
49
2
59
0
0
3
63
4
16
4
65
6
36
5
58
-1
1
6
55
-4
16
7
62
3
9
8
63
4
16
9
53
-6
36
10
59
0
0
11
57
-2
4
12
61
2
4
13
60
1
1
14
59
0
0
Total
826
0
188
Mean
59
s^2
14.46
s
3.803
tcrit
2.16
tcrit x s/sqrtn
2.196
Lower Bound
56.8
Upper Bound
61.2
i
xi
(xi-Xbar)
(xi-Xbar)^2
1
52
-7
49
2
59
0
0
3
63
4
16
4
65
6
36
5
58
-1
1
6
55
-4
16
7
62
3
9
8
63
4
16
9
53
-6
36
10
59
0
0
11
57
-2
4
12
61
2
4
13
60
1
1
14
59
0
0
Total
826
0
188
Mean
59
s^2
14.46
s
3.803
tcrit
2.16
tcrit x s/sqrtn
2.196
Lower Bound
56.8
Upper Bound
61.2
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