# How many people for a state? ⌘ Name:

The following data was provided by the Office of Statistics. The data is based on the preliminary counts from the 2010 Federated States of Micronesia census. The data examines the populations of municipalities in Pohnpei versus Kosrae and the loss of overall population on Kosrae. Implicit in this analysis are questions such as, "How much population should constitute a municipality?" "Is there a point at which a municipality is too small to be considered a municipality." Possibly the most sensitive implied question is, "If the population of Kosrae is smaller than or on par with a single Pohnpeian municipal population, should not Kosrae return to being a municipality?"

Data sheet

Part I: For questions one to four, use the Pohnpei data only.

PohnpeiPop
Sokehs6640
Nett6542
Kitti6470
Kolonia6068
U3192
1. __________ Find the sample size n.
2. __________ Find the sample sum.
3. __________ Find the median.
4. __________ Find the sample mean x.

Part II: For questions five to eight, use the Kosrae data only.

KosraePop
Tafunsak2173
Lelu2160
Malem1300
Utwe982
1. __________ Find the sample size n.
2. __________ Find the sample sum.
3. __________ Find the median.
4. __________ Find the sample mean x.
5. __________ The sum is the population of each of the main islands. Are there municipalities on Pohnpei with a larger population than the state of Kosrae?

Part III: For the following questions, use all the population data in the table below.

PohnpeiPopKosraePop
Sokehs6640Tafunsak2173
Nett6542Lelu2160
Kitti6470Malem1300
Kolonia6068Utwe982
U3192
1. _________ Determine the sample size n.
2. _________ Determine the minimum.
3. _________ Determine the maximum.
4. _________ Calculate the range.
5. _________ Determine the class width. Use six classes (bins or intervals).
6. Fill in the following table with the class upper limits in the first column, the frequencies in the second column, and the relative frequencies in the third column
Classes (x)Frequency fRel Freq p(x)
Sums:
7. Sketch a histogram of the relative frequency data.
8. __________________ What is the shape of the distribution?

Part IV: In the following section, use the Pohnpei municipal data.

PohnpeiPop
Sokehs6640
Nett6542
Kitti6470
Kolonia6068
U3192
1. __________ Find the sample size n.
2. __________ Find the sample mean x.
3. __________ Find the sample standard deviation sx.
4. __________ Find the coefficient of variation CV.
5. _________ Calculate the standard error of the sample mean x
6. _________ Find tcritical for a confidence level c of 95%
7. _________ Determine the margin of error E for the sample mean x.
8. Write out the 95% confidence interval for the population mean μ
p(_____________ < μ < ___________) = 0.95
9. _________ Based on the confidence interval above, is the Kosrae municipality mean size of 1654 within the 95% confidence interval for the mean size of a Pohnpei municipality?
10. ___________ Is the Kosraean mean municipality size too small or too large compared to the mean size of a Pohnpeian municipality?
11. _________ Based on the confidence interval above, is the entire population of Kosrae of 6615 within the 95% confidence interval for the mean size of a Pohnpei municipality?
12. _________ Which is true, A or B?
A. The population size of a Kosrae state municipality is statistically equivalent to the population size of a Pohnpei state municipality.
OR
B. The population size of the entire population of Kosrae state is statistically equivalent to the population size of a Pohnpei state municipality.

## Part V: Hypothesis Testing using the t-test

In part five you will run a two sample hypothesis test on whether there is a statistically significant difference between two independent samples using a risk of a type I error alpha α = 0.05 The sample data is the size of the municipalities in Pohnpei versus Kosrae state. The test will determine whether the municipalities could come from a single population with a single mean. In other words, based on the means, are the population sizes of the municipalities in the two states equivalent or statistically significantly different? Use a two-tailed t-test for two independent samples.

PohnpeiKosrae
Sokehs6640Tafunsak2173
Nett6542Lelu2160
Kitti6470Malem1300
Kolonia6068Utwe982
U3192
1. _________ Calculate the sample mean x for a Pohnpei municipality.
2. _________ Calculate the sample mean x for a Kosrae municipality.
3. _________ Are the sample means for the two samples mathematically different?
4. __________________ What is the p-value? Use the TTEST function with two tails to determine the p-value for this two sample data.
5. __________________ Is the difference in the means statistically significant at a risk of a type I error alpha α = 0.05?
6. __________________ Would we fail to reject | or | reject a null hypothesis of no difference in the sample means?
7. __________________ What is the maximum level of confidence we can have that the difference in the means is statistically significant?
8. __________________ Based on the t-test, are the means statistically equivalent?

## Part VI: Linear Regression

The table contains data on the population of Kosrae from 1980 to 2000. Use this data in this section.

YearPopulation
19805500
19866607
19947317
20007686
1. _________ Calculate the slope of the linear regression (best fit line).
2. _________ Calculate the y-intercept of the linear regression (best fit line).
3. _________ Is the relation positive, negative, or neutral?
4. _________ Calculate the linear correlation coefficient r for the data.
5. ______________ Is the correlation none, weak/low, moderate, strong/high, or perfect?
6. ______________ Determine the coefficient of determination.
7. ______________ What percent in the variation in year "explains" the variation in population?
8. _________ Use the slope and intercept to predict the population in the year 2010.
9. _________ Use the slope and intercept to determine the population in the year 2020.

Part VII: The table contains data on the population of Kosrae from 2000 to 2010. Use this data in this section.

YearPopulation
20007686
20106616
1. _________ Calculate the slope of the linear regression (best fit line).
2. _________ Calculate the y-intercept of the linear regression (best fit line).
3. _________ Is the relation positive, negative, or neutral?
4. _________ Use the slope and intercept to predict the population in the year 2020.
5. _________ Is the year 2020 projection in #50 the same as the year 2020 projection in #46?
6. _________ The projected year 2020 population in Kosrae calculated in #50 would put the population of Kosrae below which Pohnpei municipality in rank order?
7. _________ Use the slope and intercept to predict the year in which the population of Kosrae state will be 0.