3. Grade point averages are believed to be normally distributed with mean. The university conducted a survey to see whether the mean GPA of sophomores is different from that of juniors. By SRS, the university collect 18 sophomores and 14 juniors and the data of GPAS is shown below (For R, you can use GPAS.csv). Assume that Sophormore = X1, Junor = X2 3.04 2.92 2.86 1.71 3.6 3.49 3.3 2.28 3.11 X1 X2 Sophomore 2.88 2.82 2.13 2.11 3.03 3.27 2.6 3.13 2.83 sample mean 2.56 3.47 2.65 2.77 3.26 2.7 3.2 3.39 sample stdev. Junior 3.19 2.58 2.98 3.13 sample size t* df (a) What is a 95% confidence interval for u1- µ2 ? Lower Bound (Limit) Upper Bound (Limit) (Use the conservative value for the degrees of freedom and round it to two decimal places) (b) At the 5% significance level, do the data provide sufficient evidence to conclude that the mean GPAS of sophomores and juniors at the university differ? In other words, the school will test HO: µ1 = µ2, Ha: µ1 # µ2 where 1=sophomore and 2 = junior (Assume that two sample t-procedures are safe to use, unequal variance). The numerical value of the two-sample t statistic is: (use the conservative value for the degrees of freedom). (c) What is the P-value of this test? 1) Conclusion of the test: (d) What is your conclusion of the test? (statistical conclusion and its interpretation). Is it consistent with the conclusion of a 95% confidence interval for µ1-µ2? (Note: "Consistency" means the conclusion of test of significance is the same as the conclusion of the confidence interval. So, need to find yourself what the conclusion of Cl is) 2) Consistent?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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answers 3c 3d 3e

3. Grade point averages are believed to be normally distributed with mean. The university conducted a survey to see
whether the mean GPA of sophomores is different from that of juniors. By SRS, the university collect 18 sophomores
and 14 juniors and the data of GPAS is shown below (For R, you can use GPAS.csv).
Assume that Sophormore = X1, Junor = X2
3.04
2.92
2.86
1.71
3.6
3.49
3.3
2.28
3.11
X1
X2
Sophomore
2.88
2.82
2.13
2.11
3.03
3.27
2.6
3.13
2.83
sample mean
2.56
3.47
2.65
2.77
3.26
2.7
3.2
3.39
sample stdev.
Junior
3.19
2.58
2.98
3.13
sample size
t*
df
(a) What is a 95% confidence interval for u1- µ2 ?
Lower Bound (Limit)
Upper Bound (Limit)
(Use the conservative value for the degrees of freedom and round it to two decimal places)
(b) At the 5% significance level, do the data provide sufficient evidence to conclude that the mean GPAS of sophomores and
juniors at the university differ? In other words, the school will test HO: µ1 = µ2, Ha: µ1 # µ2 where 1=sophomore and 2 = junior
(Assume that two sample t-procedures are safe to use, unequal variance).
The numerical value of the two-sample t statistic is: (use the conservative value for the degrees of freedom).
(c) What is the P-value of this test?
1) Conclusion of the test:
(d) What is your conclusion of the test? (statistical conclusion and its interpretation). Is it consistent with the conclusion of a
95% confidence interval for µ1-µ2? (Note: "Consistency" means the conclusion of test of significance is the same as the
conclusion of the confidence interval. So, need to find yourself what the conclusion of Cl is)
2) Consistent?

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