1. https://illinois. 5-essentials
- Click “Take the 5 essentials survey” button at top right - Select student survey on left - Enter info --Use Madison for county

2. Sections 9.4 and 9.5

3. Page 634, E58

4. Page 634, E58
a) These are not independent random samples of men and women but an observational study conducted by looking at medical charts in one city.

5. Page 634, E58
a) These are not independent random samples of men and women but an observational study conducted by looking at medical charts in one city.
Both boxplots are fairly symmetrical so the underlying populations probably are approximately normal. There is one outlier for the males.

6. Page 634, E58
a) The populations of men and women are larger than 10 times their sample sizes (respectively 10(91) = 910 and 10(84) = 840)

7. Page 634, E58
State hypotheses.

8. Page 634, E58 State hypotheses.
Ho: µf = µm, where µf is the mean calcium level in the blood of women and µm is the mean calcium level in the blood of men

9. Page 634, E58 State hypotheses.
Ho: µf = µm, where µf is the mean calcium level in the blood of women and µm is the mean calcium level in the blood of men
Ha: µf > µm

10. 2-SampTTest x1: 2.3969048 sx1: 0.14049805 n1: 84 x2: 2.3181319 sx2: 0.12172749 n2: 91 u1: >u2

11. Page 634, E58
t ; P-value
3.95

12. Page 634, E58
Interpret P-value: If these could be considered independent random samples of men and women and if there was no difference between the mean calcium levels in the blood of men and women, the probability of a t-statistic of 3.95 or larger with samples of 84 women and 91 men is

13. Page 634, E58
Interpret P-value: If these could be considered independent random samples of men and women and if there was no difference between the mean calcium levels in the blood of men and women, the probability of a t-statistic of 3.95 or larger with samples of 84 women and 91 men is However, because this was an observational study, these results are questionable.

14. Page 636, E61

15. Page 636, E61 Check conditions: These are random
samples and presumably independent as no indication of any pairing taking place.

16. Page 636, E61

17. Page 636, E61 The boxplots of the data show one unusually
small heart rate for the males. This may
cause problems, so the analysis will be
done with and without this outlier.
Otherwise, the distributions look fairly
symmetric. So, it’s reasonable to assume
these samples came from normally
distributed populations.

18. Page 636, E61
Also, both populations are more than 10 times the respective sample sizes as there are more than 10(13) = 130 men and 130 women.
So the conditions for inference are met.

19. Use 2-SampTInt

20. Page 636, E61
I’m 95% confident that the difference between the mean heart rate for all men in this population and the mean heart rate for all women in this population is in the interval (- 4.71, 9.94).

21. Page 636, E61
I’m 95% confident that the difference between the mean heart rate for all men in this population and the mean heart rate for all women in this population is in the interval (- 4.71, 9.94).
If the outlier among the men’s heart rates is
dropped, the 95% confidence interval for the
difference in means becomes (- 2.76, 10.94)

22. Page 636, E61
Because 0 is in both of these intervals, there may not be any difference between the mean heart rates of the men and the women in these populations.

23. Page 636, E61
Now, do significance test

24. Page 636, E61
Two-sided significance test for the difference of two means

25. Page 636, E61
Conditions checked for CI. Met with one concern about outlier in men’s heart rate sample.

26. Page 636, E61

27. Page 636, E61

28. Page 636, E61 Write a conclusion in context:
I do not reject the null hypothesis because
the P-value of is larger than the
significance level of 0.05.
There is not sufficient evidence to say that the mean heart rates differ for the two groups.

29. Page 636, E61 With the outlier removed, t ±1.259
and the P-value is about 0.22.

30. Page 636, E61 I do not reject the null hypothesis because
the P-value of 0.22 is larger than the
significance level of 0.05.
There is not sufficient evidence to say that the mean heart rates differ for the two groups.
Our conclusion stays the same in both cases.

31. Page 636, E61 The results of our CI and significance test
both state there is no statistically significant
evidence of a difference between the two
population means.

32. Page 655, E71

33. Page 655, E71 a. You should use one-sample procedures
for the mean of the differences because you
have the results of both treatments for each
team.
This is a repeated measures design.

34. Page 655, E71 b. Randomization in this situation means
that the order of the treatments was
randomly assigned, which is the case here.

35. Page 655, E71

36. Page 655, E71 b. The distribution of distances has no
outliers and acceptable skewness.
The conditions for inference are met.

37. Page 655, E71
Use TInterval
L3 = L2 – L1

38. Page 655, E71
The 95% CI is ( , )

39. Page 655, E71 I’m 95% confident that the mean of the
differences distance of a bear launched
using four books and the distance of a bear
launched using one book is between
and in.
Because 0 is in the interval, the evidence
isn’t sufficient to support the claim that
launch angle makes a difference in how far
gummy bears soar.

40. Page 656, E74

41. Page 656, E74 a.
The treatments were assigned in random order to the subjects.
The distributions of both lists are very symmetric with no outliers.
The conditions are met for a two-sample significance test.

42. Page 656, E74

43. Page 656, E74
Use 2-SampTTest
Inpt: Data L1 L2
Pooled: No

44. Page 656, E74

45. Page 656, E74

46. Page 656, E74

47. Page 656, E74
L3 = L1 – L2
Use T-Test
Inpt: Data L3

48. Page 656, E74

49. Page 656, E74
e. The one-sample test on the differences has more power because the P-value is smaller, meaning the null hypothesis is more likely to be rejected.

50. Questions?