Elementary Statistics: A Step By Step Approach
Elementary Statistics: A Step By Step Approach
10th Edition
ISBN: 9781259755330
Author: Allan G. Bluman
Publisher: McGraw-Hill Education
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Chapter 14.1, Problem 19E
To determine

The sample mean of number of electoral votes.

To compare: The sample mean with the population mean.

Expert Solution & Answer
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Answer to Problem 19E

The mean of number of electoral votes is 5.9.

There is a large difference between the sample mean and population mean and this is because of the large variation between the observations.

Explanation of Solution

Answers will vary. One of the possible answers is given below:

There are many ways to divide the population into clusters. Here, the population is divided into cluster based on some interval values of number of electoral votes.

Procedure for selecting the 10 samples by using cluster sampling is as follows.

  • In the data the highest value of number of electoral votes is 55 and least value of number of electoral votes is 3.

    Range = highest valuelowest value=553=52

  • Divide the data into 5 clusters, based on the range of unemployment rates.
  • The range obtained is 52.  Divide the range by 5 to get 10.4.
  • Arrangement ofintervals with range 10.4 as follows.
3-13.4
13.5-23.8
23.9-34.2
34.3-44.6
44.7-55
  • Arrange all the values of number of electoral votes according to the intervals and each interval is named as cluster1, cluster2, cluster3, cluster4, cluster5.
  • The following table represents the 5 clusters, which are arranged according to the intervals.

Cluster1:

States Number of electoral votes
AL 9
AK 3
AZ 11
AR 6
CO 9
CT 7
DE 3
DC 3
HI 4
TD 4
TN 11
KS 6
KY 8
IA 6
LA 8
ME 4
MD 10
MA 11
MN 10
MS 6
MO 10
MT 3
NE 5
NV 6
NH 4
NM 5
ND 3
OK 7
OR 7
RI 4
SC 9
SD 3
TN 11
UT 6
VT 3
VA 13
WA 12
WV 5
WI 10
WY 3

Cluster2:

States Number of electoral votes
GA 16
IL 20
MI 16
NJ 14
NC 15
OH 18
PA 20

Cluster3:

States Number of electoral votes
FL 29
NY 29

Cluster4:

States Number of electoral votes
TX 38

Cluster 5:

States Number of electoral votes
CA 55
  • From the above clusters select the first 10 observations of Cluster 1 as a sample.
States Number of electoral votes
AL 9
AK 3
AZ 11
AR 6
CO 9
CT 7
DE 3
DC 3
HI 4
TD 4

Calculation:

To calculate mean for number of electoral votes for the selected sample is

States Number of electoral votes
AL 9
AK 3
AZ 11
AR 6
CO 9
CT 7
DE 3
DC 3
HI 4
TD 4
Total 59

The sample mean of the number of electoral votes is,

samplemeanofnumber of electoral votes=SumofthevaluesofnumberofelectorolvotesNumberofobservatiosinsample=5910=5.9

The population mean is,

populationmean=SumofallobservationsTotalnumberofobservations=53851=10.55

The Sample mean of number of electoral votes is 5.9, and the population mean of number of electoral votes is10.55.

Comparison of means:

It is clear that the sample there is large difference between the sample and the population means in the average population.

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Chapter 14 Solutions

Elementary Statistics: A Step By Step Approach

Ch. 14.1 - List the advantages and disadvantages of cluster...Ch. 14.1 - Teacher Data Using the table of random numbers,...Ch. 14.1 - Prob. 12ECh. 14.1 - Teacher Data Select a cluster sample of 10 states,...Ch. 14.1 - Record High Temperatures Which method of sampling...Ch. 14.1 - Prob. 16ECh. 14.1 - Electoral Votes Select a systematic sample of 10...Ch. 14.1 - Electoral Votes Divide the 50 states into five...Ch. 14.1 - Prob. 19ECh. 14.1 - Define sampling or selection bias.Ch. 14.1 - Prob. 22ECh. 14.1 - Define nonresponsive bias.Ch. 14.1 - Prob. 24ECh. 14.1 - Define response or interview bias.Ch. 14.1 - Prob. 26ECh. 14.1 - Define volunteer bias.Ch. 14.1 - Give an example of how volunteer bias might occur.Ch. 14.2 - Prob. 1ACCh. 14.2 - Prob. 1ECh. 14.2 - Prob. 2ECh. 14.2 - Prob. 3ECh. 14.2 - Prob. 4ECh. 14.2 - Prob. 5ECh. 14.2 - Prob. 6ECh. 14.2 - Prob. 7ECh. 14.2 - Prob. 8ECh. 14.2 - Prob. 9ECh. 14.2 - Exercises 1 through 9 include questions that...Ch. 14.2 - Prob. 11ECh. 14.2 - Exercises 1 through 9 include questions that...Ch. 14.2 - Prob. 13ECh. 14.2 - Prob. 14ECh. 14.2 - Prob. 15ECh. 14.2 - Exercises 1 through 9 include questions that...Ch. 14.2 - Prob. 17ECh. 14.2 - Prob. 18ECh. 14.2 - Prob. 19ECh. 14.3 - Simulations Answer the following questions: 1....Ch. 14.3 - Prob. 1ECh. 14.3 - Prob. 2ECh. 14.3 - Who is responsible for the development of modern...Ch. 14.3 - Prob. 4ECh. 14.3 - Prob. 5ECh. 14.3 - Prob. 6ECh. 14.3 - Prob. 7ECh. 14.3 - Prob. 8ECh. 14 - Hurricanes Select a random sample of eight storms...Ch. 14 - Prob. 14.1.2RECh. 14 - Hurricanes Select a cluster of 10 storms. Compute...Ch. 14 - Prob. 14.1.4RECh. 14 - Prob. 14.1.5RECh. 14 - Prob. 14.1.6RECh. 14 - Prob. 14.1.8RECh. 14 - Prob. 14.2.9RECh. 14 - Prob. 14.2.10RECh. 14 - Prob. 14.2.11RECh. 14 - Prob. 14.2.12RECh. 14 - Prob. 1DACh. 14 - Prob. 2DACh. 14 - Select a cluster sample of 20 individuals, and...Ch. 14 - Prob. 4DACh. 14 - Prob. 5DACh. 14 - Determine whether each statement is true or false....Ch. 14 - Prob. 2CQCh. 14 - Prob. 3CQCh. 14 - Prob. 4CQCh. 14 - Prob. 5CQCh. 14 - Prob. 6CQCh. 14 - Interviewing selected people at a local...Ch. 14 - Prob. 8CQCh. 14 - Prob. 9CQCh. 14 - Prob. 10CQCh. 14 - Blood Pressure Select a random sample of 12...Ch. 14 - Prob. 12CQCh. 14 - Blood Pressure Divide the individuals into...Ch. 14 - Prob. 14CQCh. 14 - Prob. 25CQCh. 14 - Prob. 26CQCh. 14 - Prob. 27CQCh. 14 - Prob. 28CQCh. 14 - For Exercises 2530, explain why the survey...Ch. 14 - Prob. 30CQCh. 14 - Prob. 1DP
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