Question

In: Statistics and Probability

Q4. Calculate the mean difference in scores (After - Before) and the sample variance of the difference.

ID	After	Before
1	1230	1074
2	1090	1039
3	1028	1004
4	1230	1154
5	1200	1144
6	1030	974
7	1220	1174
8	1085	1134
9	1000	1094
10	1320	1174
11	1075	1004
12	1040	1014
13	1030	1114
14	1110	1134
15	995	1079
16	1160	1184
17	1250	1254
18	1000	994
19	1110	1024
20	1045	1004
21	925	884
22	1005	1044
23	1150	1054
24	1015	1019
25	980	934

Mean Difference ==>

Sample Variance of Difference ==>

Q5. Calculate the LCL and UCL for a 90% CI (α = 0.1) for the mean difference in scores.

LCL ==>

UCL ==>

Based on this 90% interval, would you say the prep course improved scores (Yes/No)

Q6. Calculate the LCL and UCL for a 95% CI (α = 0.05) for the mean difference in scores.

LCL ==>

UCL ==>

Based on this 95% interval, would you say the prep course improved scores (Yes/No)

Solutions

Expert Solution

Number	Before	After	Difference
	1074	1230	-156	17234.4384
	1039	1090	-51	690.6384
	1004	1028	-24	0.5184
	1154	1230	-76	2629.6384
	1144	1200	-56	978.4384
	974	1030	-56	978.4384
	1174	1220	-46	452.8384
	1134	1085	49	5434.6384
	1094	1000	94	14094.4384
	1174	1320	-146	14708.8384
	1004	1075	-71	2141.8384
	1014	1040	-26	1.6384
	1114	1030	84	11820.0384
	1134	1110	24	2373.6384
	1079	995	84	11820.0384
	1184	1160	24	2373.6384
	1254	1250	4	824.8384
	994	1000	-6	350.4384
	1024	1110	-86	3755.2384
	1004	1045	-41	265.0384
	884	925	-41	265.0384
	1044	1005	39	4060.2384
	1054	1150	-96	5080.8384
	1019	1015	4	824.8384
	934	980	-46	452.8384
Total	26705	27323	-618	103613.04

Question 4

Question 5

Confidence Interval :-

Lower Limit =
Lower Limit = -47.2027
Upper Limit =
Upper Limit = -2.2373
90% Confidence interval is ( -47.2027 , -2.2373 )
Since CI values are in negative, we would say the prep course improved.

Question 6

Confidence Interval :-

Lower Limit =
Lower Limit = -51.8417
Upper Limit =
Upper Limit = 2.4017
95% Confidence interval is ( -51.8417 , 2.4017 )
Since CI contain 0, we would say the prep course does not improved.

orchestra answered 1 year ago

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