Download Solutions to the problems in the third sample test

Sample Test #4
Math 146
Data Set #1
0.82806 3.46379 4.45048 5.72916
2.28209 3.46387 4.61693 5.82915
2.85516 3.47212 4.64214 5.89093
3.11370 3.60505 5.10139 6.01711
3.13829 4.06108 5.14685 6.19383
3.18826 4.15561 5.20364 6.87012
3.40354 4.37153 5.49842 7.69882
Summaries for this data set:
Sum
124.291
Count
28
Sum of Squares 612.300
Data Set #2
We have a second data set with the following statistics:
Mean
3.96331
Sample Variance 0.72681
Count
33
Recall: The sample standard deviation is the square root of the sample variance
Descriptive Statistics: Calculate for data set #1 only
•
Sample mean, sample standard deviation, and sample variance
•
1st Quartile, Median, and 3rd Quartile
Mean
4.43897
Standard Error
0.28307
Median
4.411
1 quartile
3.44873
3 quartile
5.55611
Standard Deviation 1.49785
Sample Variance
2.24356
Inferential Statistics (confidence and significance levels are up to you)
Confidence Interval for data set #1
Choosing a confidence level, use the previous data for a confidence interval for the “true” mean (the
variance is unknown).
Data 1
95% CI for the Mean from 3.85816
to
5.01977
Data 1
99% CI for the Mean from 3.65468
to
5.22326
Data 1
90% CI for the Mean from 3.95682
to
4.92111
Data 1
98% CI for the Mean from 3.73904
to
5.1389
Optional: If you have time left, you may also construct a confidence interval for the second data set.
left end right end
95.00% 3.66102
99.00%
4.2656
3.5569 4.36972
90.00% 3.71193 4.21469
98.00% 3.59991 4.32671
Testing for the mean for data set #2
Test the hypothesis (at a level of your choice)
H0: μ = 4.2
H0: μ < 4.2
t-score
−1.5949
p-value
0.06029
If you chose 5% (or less) as your significance level, you would not reject the Null Hypothesis, since the
t-score is higher than the critical value (or, equivalently, because the p-value is larger than 0.05)
Testing for equality of two means (clearly, this refers to both data sets)
We now want to check if the two data sets could come from “populations” (i.e., probabilistic models)
with the same “true” mean, assuming they are independent samples.
Set up a test, without assuming that the variances are equal.
Equality of means Unequal variances
m1-m2
0.47566
E
0.31961
t-score
1.48824
p-value
0.07414
(the p-value was calculated using the simplified choice for the degrees of freedom)
Optional: If you have time left, you can repeat the test, assuming, instead, that the populations have
equal variances.
Equal variances
m1-m2
0.47566
E
0.30628
t-score
1.55304
p-value
0.06288