Statistics: Concepts and Controversies
9th Edition
ISBN: 9781464192937
Author: David S. Moore, William I. Notz
Publisher: W. H. Freeman
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Chapter 3, Problem 13E
(a)
Section 1:
To determine
The 20 simple random samples of size 5 and record the number of females in each sample.
(a)
Section 1:
Expert Solution
Answer to Problem 13E
Solution: The partial output of the 20 simple random samples is shown below:
The number of females in each sample is shown below.
| Samples | Number of females | Samples | Number of females |
| Sample 1 | 2 | Sample 11 | 1 |
| Sample 2 | 1 | Sample 12 | 2 |
| Sample 3 | 2 | Sample 13 | 4 |
| Sample 4 | 3 | Sample 14 | 2 |
| Sample 5 | 1 | Sample 15 | 3 |
| Sample 6 | 2 | Sample 16 | 2 |
| Sample 7 | 3 | Sample 17 | 0 |
| Sample 8 | 1 | Sample 18 | 2 |
| Sample 9 | 1 | Sample 19 | 1 |
| Sample 10 | 2 | Sample 20 | 2 |
Explanation of Solution
To obtain the 20 simple random samples of size 5, below steps are followed in Excel.
Step 1: Write the name and the gender of the club members in the Excel spreadsheet. The snapshot is shown below:
Step 2: Label each of the members using the numbers 1,2,⋯,25. The snapshot is shown below:
Step 3: Use the formula =RANDBETWEN(Bottom, Top) to generate a single set of
To find the number of female in each sample, the label of each female member is matched with the obtained random number of each set of sample and then the number of female is counted. The number of females obtained in each set of samples are shown in the below table.
| Samples | Number of females | Samples | Number of females |
| Sample 1 | 2 | Sample 11 | 1 |
| Sample 2 | 1 | Sample 12 | 2 |
| Sample 3 | 2 | Sample 13 | 4 |
| Sample 4 | 3 | Sample 14 | 2 |
| Sample 5 | 1 | Sample 15 | 3 |
| Sample 6 | 2 | Sample 16 | 2 |
| Sample 7 | 3 | Sample 17 | 0 |
| Sample 8 | 1 | Sample 18 | 2 |
| Sample 9 | 1 | Sample 19 | 1 |
| Sample 10 | 2 | Sample 20 | 2 |
To determine
To graph: The histogram for the number of females in each set of sample.
Expert Solution
Explanation of Solution
Graph: To obtain the histogram for the obtained result in previous part, Excel is used. The below steps are followed to obtain the required histogram.
Step 1: The number of females varies from 0 to 4. The number of samples are calculated corresponding to each number of females. The number of samples with the same number of female members is clustered. The snapshot of the obtained table is shown below:
| Number of female members | Number of samples |
| 0 | 1 |
| 1 | 6 |
| 2 | 9 |
| 3 | 3 |
| 4 | 1 |
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:
Interpretation: The obtained histogram for the number of females in each set of sample follows
To determine
To find: The average number of females in 20 samples.
Expert Solution
Answer to Problem 13E
Solution: The average number of female is 1.85.
Explanation of Solution
Calculation:
The average number of females can be obtained by using the formula:
Average=Sum of(Number of female memebers×Number of samples)Total number of samples
Hence, the average number of females is calculated as:
Average=Sum of(Number of female memebers×Number of samples)Total number of samples=(0×1)+(1×6)+(2×9)+(3×3)+(4×1)20=1.85
Therefore, the average number of females in 20 samples is 1.85.
(b)
To determine
To explain: Whether the club members should be doubtful about the discrimination if any of the five tickets does not received by women.
(b)
Expert Solution
Answer to Problem 13E
Solution: The club member should suspect the discrimination if any of the five tickets does not received by women.
Explanation of Solution
The event is going to be suspected if the chance of occurrence of that event is approximately 0.05 or less. In the provided scenario, there will be one case where the set of samples does not contain any female member. As the chance is very low, the club members can suspect about the discrimination if any of the five tickets does not received by women.
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Questions
An insurance company's cumulative incurred claims for the last 5 accident years are given
in the following table:
Development Year
Accident Year 0
2018
1 2 3 4
245 267 274 289 292
2019
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2020
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2021
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2019
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2020
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2021
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2022
330
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Chapter 3 Solutions
Statistics: Concepts and Controversies
Ch. 3 - Prob. CSCh. 3 - Prob. 1CTBCh. 3 - Prob. 2CTBCh. 3 - Prob. 3CTBCh. 3 - Prob. 4CTBCh. 3 - Prob. 5CTBCh. 3 - Prob. 6CTBCh. 3 - Prob. 7CTBCh. 3 - Prob. 8ECh. 3 - Prob. 9E
Ch. 3 - Prob. 10ECh. 3 - Prob. 11ECh. 3 - Prob. 12ECh. 3 - Prob. 13ECh. 3 - Prob. 14ECh. 3 - Prob. 15ECh. 3 - Prob. 16ECh. 3 - Prob. 17ECh. 3 - Prob. 18ECh. 3 - Prob. 19ECh. 3 - Prob. 20ECh. 3 - Prob. 21ECh. 3 - Prob. 22ECh. 3 - Prob. 23ECh. 3 - Prob. 24ECh. 3 - Prob. 25ECh. 3 - Prob. 26ECh. 3 - Prob. 27ECh. 3 - Prob. 28ECh. 3 - Prob. 29ECh. 3 - Prob. 30ECh. 3 - Prob. 31ECh. 3 - Prob. 32ECh. 3 - Prob. 33ECh. 3 - Prob. 34ECh. 3 - Prob. 35ECh. 3 - Prob. 36ECh. 3 - Prob. 37ECh. 3 - Prob. 38ECh. 3 - Prob. 39ECh. 3 - Prob. 40E
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