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# (i) Create your own data set consisting of two different samples, drawn either from Census data or from Ellis Island immigration data, that contains numeric values – such as age. For each sample, make...

(i) Create your own data set consisting of two different samples, drawn either from Census data or from Ellis Island immigration data, that contains numeric values – such as age. For each sample, make the sample size no less than 5 and no greater than 35. Show details of the sourcing and context. Instructional guides for gathering the data are in Sections 2 and 4 of LN10. There is no restriction on the year of Census; however, the complete Census records are publically available for 1940 and earlier.

(ii) State the null hypotheses in words that apply to the particular topic you are addressing. Define the populations you are referencing, their approximate sizes, and how the population averages would (in principle) be computed. Perform a two-sided, two-sample t-test. Explain what you are doing as you go along.

(iii) Show the graph of the test with all features shown and labeled.

(iv) State the probabilistic meaning of your p-value, referencing (a) the numeric value of your p-value, (b) the value of test-statistic found, and (c) the relevant area in the graph of the test.

(v) State the conclusion of the test and the grounds. Summarize the reasoning behind the conclusion.

Part 2. One-sided Two-Sample z-Test of Population Proportions. (See LN10.)

Get fresh data set for this hypothesis test; please do not recycle your data from Part 1.

(i) Develop a research hypothesis to use in a one-sided two-sample test for population proportions.

(ii) Gather data from either Census or Ellis Island records. Show details of the data sourcing.

(iii) Explain where (a) population proportions will be used in the test and where (b) sample proportions will be used in the context of your setting.

(iv) Walk the reader through the hypothesis test in the context of your data. Explain how the mechanics of the test provides the answer to the question, “How far is far?” in the context of your setting.

(v) Graph the test, labeling all relevant portions.

(vi) State the probabilistic meaning of your p-value, referencing (a) the numeric value of your p-value, (b) the value of test-statistic found, and (c) the relevant area in the graph of the test.

(vii) State the conclusion of the test and the grounds. Summarize the reasoning behind the conclusion. Be specific to your setting.

(viii) To check your work, go to MathCracker website and run the appropriate program. Show the results; do they agree? https://mathcracker.com/z-test-for-two-proportions

Answered Same Day Aug 05, 2021

## Solution

Bolla V V Satyanarayana answered on Aug 07 2021
2)
One Sample Two-Sided test for Population Proportions
We take data from census data form this Link
http:
us-census.org/pu
usgenwe
census/oh/knox/1860/indx-a-z.txt
Research question: We want to test the Proportion of People whose age is under 20 in Ohio is significantly higher than the proportion of People whose age is under 20 in PA
Let P1 denote the Proportion of People whose age is under 20 in Ohio
P2 denote the Proportions of whose age is under 20 in PA country
1.Null hypothesis: Proportion of People whose age is under 20 in Ohio is not significantly higher than the proportion of People whose age is under 20 in PA Country
2. Alternative Hypothesis: Proportion of People whose age is under 20 in Ohio is significantly higher than the proportion of People whose age is under 20 in PA Country
3.Level of significance : We take Level of significance value = 0.05
4.Test statistic: Under ,The test statistic value can be defined as
Using Excel function to find Critical value of Z:
Critical of Z =
5.Decison: Here we observe that The test statistics value of z(3.20) > Critical value of Z(1.64).So we reject the null hypothesis
6.Conclusion: Therefore we conclude that there is a sufficient evidence to support that the Proportion of People whose age is under 20 in Ohio is not significantly higher than the proportion of People whose age is under 20 in PA Country
Graph of Z-test , Critical and P-value:
Test statistic value for Right tailed = 3.20
Critical value of Right tailed = 1.64
P-value for Right tailed (One tailed) = 0.007
Level of significance value of...
SOLUTION.PDF