Question

Question 1

A student organization wants develop a program for students who are going to graduate in the next 18 months.   To get a sense of how many students might be interested in the program, they want an estimate of the proportion of students who are going to graduate in the next 18 months. They take a simple random sample of 89 students. The data they collected can be found in the column labeled “Graduate in the next 18 month”.   “No” means that the student will not graduate in the next 18 months and would not be of interest to the student organization.   “Yes” means that the student will graduate in the next 16 months and would be of interest to the student organization.

1. The vice president of the student organization has asked you to create an estimate of the proportion of students who will graduate in 18 months. You ask her what level of confidence she wants to have in the estimate and she says that she would like to be 90% confident in the proportion estimate. Create the confidence interval using the sample data. Write a sentence or two to communicate the results to her.

Question 2

A student organization wants to get an estimate of the proportion of students who would attend a Tiny Cowboys concert at Al Lang stadium.   They ask you how many students they should include in their sample to get this estimate.

1. They tell you that a similar concert held at another college close by had 24% of all students attend the concert, they would be ok with being 90% confident and want the estimate to be within 6% of the true value. Calculate the sample size. Write a sentence or two to communicate to the student organization how many students that they should sample.

Question 3

The Student Government Association is interested in an estimate of the mean hours students work per week. They take a simple random sample of 89 students. The data they collected can be found in the column labeled “Number of hours worked per week”.

1. Use the sample data to construct a 95% confidence interval for the mean number hours worked. Write one or two sentences to communicate to the Student Government the estimate and the margin of error.

Question 4

An administrator said that he believes more than 25% of all students will graduate in the next 18 months.

Use the data found in the column labeled “Graduate in the next 18 months” to answer the following questions. “No” means that the student will not graduate in the next 18 months.   “Yes” means that the student will graduate in the next 18 months.

Write the claim in symbolic form

1. Write the null and alternative hypothesis in symbolic form
2. State the test statistic
3. State the p-value
4. State your conclusion about the null hypothesis using a 0.05 significance level
5. Write a sentence to communicate to the administrator your conclusion about his claim

Data:

Students- Graduate in 18 mo- number of hours worked per week

1   No   6.3
2   No   30.1
3   No   15.8
4   No   29.1
5   No   22.6
6   No   13.8
7   No   25.4
8   No   13.1
9   No   25.4
10   No   25.3
11   No   20.6
12   No   31.2
13   No   18.1
14   No   38.1
15   No   22
16   No   33.1
17   No   15.7
18   No   33.9
19   No   21.8
20   No   22.5
21   No   27.1
22   No   25.8
23   No   25.9
24   No   17.2
25   No   28.1
26   No   16.8
27   No   24.8
28   No   37
29   No   15.9
30   No   12.6
31   No   34.7
32   No   23.7
33   No   31.8
34   No   17.7
35   No   19
36   No   35
37   No   33
38   No   10.8
39   No   24.5
40   No   26.9
41   No   31.8
42   No   22.2
43   No   21.8
44   No   26.1
45   No   25.7
46   No   31.4
47   No   25.5
48   No   18.1
49   No   31
50   No   19.8
51   No   15.9
52   No   16.8
53   No   25.4
54   No   21.3
55   No   25
56   No   20.2
57   No   4.8
58   No   37.2
59   No   19.4
60   No   15.7
61   No   18.1
62   No   13.3
63   Yes   31.7
64   Yes   19
65   Yes   23.6
66   Yes   28.4
67   Yes   17.1
68   Yes   26.7
69   Yes   7.1
70   Yes   44.7
71   Yes   31.2
72   Yes   32.7
73   Yes   15.9
74   Yes   19.4
75   Yes   25.6
76   Yes   28.9
77   Yes   27.6
78   Yes   18
79   Yes   29.5
80   Yes   23.6
81   Yes   36.5
82   Yes   41.4
83   Yes   19.6
84   Yes   11.3
85   Yes   29
86   Yes   14.4
87   Yes   27
88   Yes   41.4
89   Yes   13.1

Answer 1

Question 1

A student organization wants develop a program for students who are going to graduate in the next 18 months.   To get a sense of how many students might be interested in the program, they want an estimate of the proportion of students who are going to graduate in the next 18 months. They take a simple random sample of 89 students. The data they collected can be found in the column labeled “Graduate in the next 18 month”.   “No” means that the student will not graduate in the next 18 months and would not be of interest to the student organization.   “Yes” means that the student will graduate in the next 16 months and would be of interest to the student organization.

1. The vice president of the student organization has asked you to create an estimate of the proportion of students who will graduate in 18 months. You ask her what level of confidence she wants to have in the estimate and she says that she would like to be 90% confident in the proportion estimate. Create the confidence interval using the sample data. Write a sentence or two to communicate the results to her.

One-Way Summary Table
Count of Variable
Variable	Total	Percentage
No	62	69.66%
Yes	27	30.34%
Grand Total	89

Confidence Interval Estimate for the Proportion
Data
Sample Size	89
Number of Successes	27
Confidence Level	90%
Intermediate Calculations
Sample Proportion	0.303370787
Z Value	1.645
Standard Error of the Proportion	0.0487
Interval Half Width	0.0802
Confidence Interval
Interval Lower Limit	0.2232
Interval Upper Limit	0.3835

90% confident in the proportion estimate = (0.2232, 0.3835).

We are 90% confident that true proportion of students who will graduate in 18 months falls in the interval (0.2232, 0.3835).

Question 2

A student organization wants to get an estimate of the proportion of students who would attend a Tiny Cowboys concert at Al Lang stadium.   They ask you how many students they should include in their sample to get this estimate.

1. They tell you that a similar concert held at another college close by had 24% of all students attend the concert, they would be ok with being 90% confident and want the estimate to be within 6% of the true value. Calculate the sample size. Write a sentence or two to communicate to the student organization how many students that they should sample.

Sample size calculation

p=0.24

For 90%, z=1.645

d=0.06

Sample size = (z²*p*(1-p))/d²

= (1.645²*0.24*0.76)/0.06²

=137.105

The sample size required= 138

The required sample size to estimate of the proportion of students who would attend a Tiny Cowboys concert at Al Lang stadium with 90% confident and within 6% of the true value is 138.

Question 3

The Student Government Association is interested in an estimate of the mean hours students work per week. They take a simple random sample of 89 students. The data they collected can be found in the column labeled “Number of hours worked per week”.

1. Use the sample data to construct a 95% confidence interval for the mean number hours worked. Write one or two sentences to communicate to the Student Government the estimate and the margin of error.

Confidence Interval Estimate for the Mean
Data
Sample Standard Deviation	8.182006467
Sample Mean	23.85505618
Sample Size	89
Confidence Level	95%
Intermediate Calculations
Standard Error of the Mean	0.867290951
Degrees of Freedom	88
t Value	1.9873
Interval Half Width	1.7236
Confidence Interval
Interval Lower Limit	22.1315
Interval Upper Limit	25.5786

We are 95% confidence that true the mean number hours worked falls in the interval (22.1315, 25.5786).

The margin of error is 1.7236.

Question 4

An administrator said that he believes more than 25% of all students will graduate in the next 18 months.

Use the data found in the column labeled “Graduate in the next 18 months” to answer the following questions. “No” means that the student will not graduate in the next 18 months.   “Yes” means that the student will graduate in the next 18 months.

Write the claim in symbolic form

Write the null and alternative hypothesis in symbolic form

Ho: P=0.25 H1: P>0.25

State the test statistic

z = 1.1628

State the p-value

P=0.1225

State your conclusion about the null hypothesis using a 0.05 significance level

Ho is not rejected.

Write a sentence to communicate to the administrator your conclusion about his claim

There is no evidence in the data to support the claim of the administrator.

Z Test of Hypothesis for the Proportion
Data
Null Hypothesis            p =	0.25
Level of Significance	0.05
Number of Items of Interest	27
Sample Size	89
Intermediate Calculations
Sample Proportion	0.303370787
Standard Error	0.0459
Z Test Statistic	1.1628
Upper-Tail Test
Upper Critical Value	1.645
p-Value	0.1225
Do not reject the null hypothesis