Concept explainers
(a)
Section 1:
To find: The 20 simple random samples of size 5 and record the number of instate students in each sample.
(a)
Section 1:
Answer to Problem 14E
Solution: The partial output of 20 simple random samples is shown below:
The number of instate players obtained in each set of samples is shown in the below table.
Samples | Number of instate players | Samples | Number of instate players |
Sample 1 | 2 | Sample 11 | 4 |
Sample 2 | 1 | Sample 12 | 1 |
Sample 3 | 2 | Sample 13 | 3 |
Sample 4 | 2 | Sample 14 | 0 |
Sample 5 | 1 | Sample 15 | 2 |
Sample 6 | 0 | Sample 16 | 0 |
Sample 7 | 3 | Sample 17 | 3 |
Sample 8 | 3 | Sample 18 | 2 |
Sample 9 | 1 | Sample 19 | 3 |
Sample 10 | 4 | Sample 20 | 3 |
Explanation of Solution
Calculation:
Step 1: In the Excel spreadsheet, write the name of the students and whether they are instate players or not. The snapshot is shown below:
Step 2: Label each of the students using the numbers
Step 3: Use the formula
To find the number of instate players in each sample, the label of each instate players are matched with the obtained random number of each set of sample and calculate the number of instate players. The number of instate players obtained in each set of samples are shown in the below table.
Samples | Number of instate players | Samples | Number of instate players |
Sample 1 | 2 | Sample 11 | 4 |
Sample 2 | 1 | Sample 12 | 1 |
Sample 3 | 2 | Sample 13 | 3 |
Sample 4 | 2 | Sample 14 | 0 |
Sample 5 | 1 | Sample 15 | 2 |
Sample 6 | 0 | Sample 16 | 0 |
Sample 7 | 3 | Sample 17 | 3 |
Sample 8 | 3 | Sample 18 | 2 |
Sample 9 | 1 | Sample 19 | 3 |
Sample 10 | 4 | Sample 20 | 3 |
Section 2:
To graph: The histogram for the number of instate players in each set of sample.
Section 2:
Answer to Problem 14E
Solution: The obtained histogram is obtained as:
Explanation of Solution
Graph:
To obtain the histogram for the obtained result in previous part, Excel is used. The below steps are followed to obtained the required histogram.
Step 1: The number of instate players varies from 0 to 4. The number of samples are calculated corresponding to each number of instate players. The number of samples with same number of instate players are clustered. The snapshot of the obtained table is shown below:
Number of instate players members | Number of samples |
0 | 3 |
1 | 4 |
2 | 5 |
3 | 6 |
4 | 2 |
Step 2: Select the data set and go to insert and select the option of cluster column under the Recommended Charts. The screenshot is shown below:
Step 3: Click on OK. The diagram is obtained as:
Step 4: Click on the chart area and select the option of “Primary Horizontal” and “Primary Vertical” axis under the “Add Chart Element” to add the axis title. The screenshot is shown below:
Step 5: Click on the bars of the diagrams and reduce the gap width to zero under the “Format Data Series” tab. The screenshot is shown below:
The obtained histogram is:
Section 3:
To find: The average number of instate players in 20 samples.
Section 3:
Answer to Problem 14E
Solution: The average number of instate players is 2.
Explanation of Solution
Explanation
Calculation:
The average number of instate players can be obtained by using the formula:
Hence, the average number of instate players is calculated as:
(b)
To explain: Whether the college should be doubtful about the discrimination if any of the five scholarships does not received by instate players.
(b)
Answer to Problem 14E
Solution: The college should suspect the discrimination if any of the five scholarships does not received by instate players.
Explanation of Solution
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Chapter 3 Solutions
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