Assume you need to build a confidence interval for a population mean within some given situation. Naturally, you must determine whether you should use either the t-distribution or the z-distribution or possibly even neither based upon the information known/collected in the situation. Thus, based upon the information provided for each situation below, determine which ( t -, z - or neither) distribution is appropriate. Then if you can use either a t- or z- distribution, give the associated critical value (critical t - or z - score) from that distribution to reach the given confidence level. a. 99% confidence n=150 σ known population data believed to be very skewed Appropriate distribution: Associated critical value: b. 95% confidence n=10 σ unknown population data believed to be normally distributed Appropriate distribution: Associated critical value: c. 90% confidence n=40 σ unknown population data believed to be normally distributed Appropriate distribution: Associated critical value: d. 99% confidence n=12 σ unknown population data believed to be very skewed Appropriate distribution: Associated critical value: A student researcher is interested in determining the average ( µ ) GPA of all FHSU students, in order to investigate grade inflation at regional universities. The data below represent the GPA's of thirty-six randomly selected FHSU students. 2.75 2.55 3.95 1.74 2.66 3.10 2.41 1.57 2.12 3.67 3.56 1.98 4.00 3.21 1.95 3.75 1.45 3.01 2.29 2.66 3.95 2.50 3.88 2.79 2.32 3.44 2.07 0.62 2.72 3.55 3.92 3.41 2.14 1.15 2.75 3.25 a. How do you know that you will need to construct the confidence interval using a t -distribution approach as opposed to a z -distribution? We want to construct the mean value confidence interval for the GPA's with a 90% confidence level. b. Determine the best point estimate (average) for the mean GPA. c. Determine the critical t -value(s) associated with the 95% confidence level. d. Determine the margin of error. e. Determine the confidence interval. f. In a sentence, interpret the contextual meaning of your result to part e above...that is relate the values to this situation regarding the mean GPA's of all FHSU students. Determine the two chi-squared ( χ 2 ) critical values for the following confidence levels and sample sizes. a. 95% and n =30 b. 99% and n =20 ...

1. Assume you need to build a confidence interval for a population
mean within some given situation.
Naturally, you must determine whether you should use either
the t-distribution or the z-distribution or possibly even neither
based upon the information known/collected in the situation.
Thus, based upon the information provided for each situation
below, determine which (
t
-,
z
- or neither) distribution is appropriate.
Then
if
you can use either a t- or z- distribution, give the associated
critical value (critical
t
- or
z
- score) from that distribution to reach the given confidence
level.

3. a.
99% confidence
n=150
σ known
population data believed to be very skewed
Appropriate distribution:
Associated critical value:

4. b.
95% confidence
n=10
σ unknown
population data believed to be normally distributed

5. Appropriate distribution:
Associated critical value:

6. c.
90% confidence
n=40
σ
unknown
population data believed to be normally distributed
Appropriate distribution:

7. Associated critical value:
d.
99% confidence

8. n=12
σ unknown
population data believed to be very skewed
Appropriate distribution:
Associated critical value:

10. A student researcher is interested in determining the average (
µ
) GPA of all FHSU students, in order to investigate grade
inflation at regional universities.
The data below represent the GPA's of thirty-six randomly
selected FHSU students.

11. 2.75
2.55
3.95
1.74
2.66
3.10
2.41
1.57
2.12
3.67
3.56
1.98
4.00
3.21
1.95
3.75
1.45
3.01
2.29
2.66
3.95
2.50
3.88
2.79
2.32
3.44
2.07

12. 0.62
2.72
3.55
3.92
3.41
2.14
1.15
2.75
3.25
a.
How do you know that you will need to construct the confidence
interval using a
t
-distribution approach as opposed to a
z
-distribution?

13. We want to construct the mean value confidence interval for the
GPA's with a 90% confidence level.

14. b.
Determine the best point estimate (average) for the mean GPA.

15. c.
Determine the critical
t
-value(s) associated with the 95% confidence level.

16. d.
Determine the margin of error.

17. e.
Determine the confidence interval.

18. f.
In a sentence, interpret the contextual meaning of your result to
part e above...that is relate the values to this situation regarding
the mean GPA's of all FHSU students.

20. Determine the two chi-squared (
χ
2
) critical values for the following confidence levels and sample
sizes.

21. a.
95% and
n
=30

22. b.
99% and
n
=20

24. We are also interested in estimating the population standard
deviation (σ) for all FHSU student GPA's.
We will assume that GPA's are at least approximately normally
distributed.
Below are the GPA's.

25. 2.75
2.55
3.95
1.74
2.66
3.10
2.41
1.57
2.12
3.67
3.56
1.98
4.00
3.21
1.95
3.75
1.45
3.01
2.29
2.66
3.95
2.50
3.88
2.79

26. 2.32
3.44
2.07
0.62
2.72
3.55
3.92
3.41
2.14
1.15
2.75
3.25
Out to the right, construct a 95% confidence interval estimate of
sigma (σ), the population standard deviation.

29. (Multiple Choice) A hypothesis test is used to test a claim.
On a right-tailed hypothesis test with a 1.39 critical value, the
collected sample's test statistic is calculated to be 1.45.
Which of the following is the correct decision statement for the
test?
A.
Fail to reject the null hypothesis

30. B.
Reject the null hypothesis
C.
Claim the alternative hypothesis is true
D.
Claim the null hypothesis is false

31. (Multiple Choice) A hypothesis test is used to test a claim.
A
P
-value of 0.08 is calculated on the hypothesis test with a
significance level set at 0.05.
Which of the following is the correct decision statement for the
test?

32. A.
Claim the null hypothesis is true
B.
Claim the alternative hypothesis is false
C.
Reject the null hypothesis

33. D.
Fail to reject the null hypothesis

34. (Multiple Choice) Which of the following is
not
a requirement for using the
t
-distribution for a hypothesis test concerning
μ
.
A.
Sample size must be larger than 30
B.
Sample is a simple random sample

35. C.
The population standard deviation is unknown

36. In an effort to promote healthy lifestyles, health screenings are
given to employees of a large corporation.
In running a promotional trial, 84 out of the 150 people who
work in
one
office for the corporation participate in the health screening.

37. a.
Is the above information sufficient for you to be completely
certain that
more than
50% of
all
employees of the corporation will participate in the health
screening?
Why or why not?

38. b.
In establishing a statistical hypothesis testing of this situation,

39. give the required null and alternative hypotheses for such a test,
if it is desired that more than 50% of the employees participate
in the health screening.
H
0
:

40. H
1
:

41. c.
Based on your answer in part b, should you use a right-tailed, a
left-tailed, or a two-tailed test? Briefly explain how one
determines which of the three possibilities is to be used.

43. d.
Describe the possible Type I error for this situation--make sure
to state the error in terms of the percent of employees in the
corporation who will participate in the health screenings.

45. e.
Describe the possible Type II error for this situation--make sure
to state the error in terms of the percent of employees in the
corporation who will participate in the health screenings.

47. f.
Determine the appropriate critical value(s) for this situation
given a 0.025 significance level.

48. g.

49. Determine/calculate the value of the sample's test statistic.

50. h.
Detemine the
P
-value.

51. i.
Based upon your work above, is there statistically sufficient
evidence in this sample to support that more than 50% of
employees will participate in the health screening?
Briefly explain your reasoning.

54. The mean score on a certain achievement test at the turn of the
century was 74.
However, national standards have been implmented which may
lead to a change in the mean score.
A random sample of 40 scores on this exam taken this year
yeilded the following data set.
At a 10% significance level, test the claim that the mean of all
current test scores is not the same as in 2000.

55. 85
77
74
88
89
66
0
70
73
76
86
74
73
82
72
0

56. 82
82
80
76
87
76
77
67
72
49
73
75
82
73
81
30

57. 58
75
72
89
76
18
72
74
a.

58. Give the null and alternative hypotheses for this test in
symbolic form.
H
0
:
H
1
:

59. b.
Determine the value of the test statistic.