Question

Solve given Inferences involving two populations Inference about two Population Proportions: Independent Samples: A government housing agency is compa

Comparing two groups
ANSWERED
asked 2020-12-05
Solve given Inferences involving two populations Inference about two Population Proportions:
Independent Samples:
A government housing agency is comparing home ownership rates among several immigrant groups. In a sample of 235 families who emigrated to the U.S. from Eastern Europe five years ago, 165 now own homes. In a sample of 195 families who emigrated to the U.S. from Pacific islands five years ago, 125 now own homes.

Answers (1)

2020-12-06

\(\displaystyle{p}_{{1}}\): Proportion of families who emigrated to the U.S. from Eastern Europe five years ago
\(\displaystyle{p}_{{2}}\): Proportion of families who emigrated to the U.S. from Pacific islands five years ago
Null hypothesis: \(\displaystyle{H}_{{0}}:{p}_{{1}}={p}_{{2}}\)
Sample 1: emigrated to the U.S. from Eastern Europe five years ago
Number families who emigrated to the U.S. from Eastern Europe five years ago: \(\displaystyle{n}_{{1}}={235}\)
Number families who now own homes: \(\displaystyle{x}_{{1}}={165}\)
Proportion of families who emigrated to the U.S. from Eastern Europe five years ago :small \(\displaystyle{w}{i}{d}{e}\hat{{{p}}}_{{{1}}}={0.7021}\)
Sample 2: emigrated to the U.S. from Pacific islands five years ago
Number families who emigrated to the U.S. from Pacific islands five years ago: \(\displaystyle{n}_{{2}}={195}\)
Number families who now own homes: \(\displaystyle{x}_{{2}}={125}\)
Sample proportion of families who emigrated to the U.S. from Pacific islands five years ago: small \(\displaystyle{w}{i}{d}{e}\hat{{{p}}}_{{{2}}}=\frac{{125}}{{195}}={0.641}\)
Test Statistic: \(\displaystyle{Z}={\frac{{\hat{{p}}_{{1}}\ -\ \hat{{p}}_{{2}}}}{{\sqrt{{{\frac{{\hat{{p}}_{{1}}\ {\left({1}-\hat{{p}}_{{1}}\right)}}}{{{n}_{{1}}}}}\ +\ {\frac{{\hat{{p}}_{{2}}\ {\left({1}-\hat{{p}}_{{2}}\right)}}}{{{n}_{{2}}}}}}}}}}\)
Test Statistic: \(\displaystyle{Z}={\frac{{{0.7021}\ -\ {0.641}}}{{\sqrt{{{\frac{{{0.7021}{\left({1}-{0.7021}\right)}}}{{{235}}}}\ +\ {\frac{{{0.641}{\left({1}-{0.641}\right)}}}{{{195}}}}}}}}}\ =\ {\frac{{{0.0611}}}{{{0.0455}}}}\ =\ {1.3429}\)
For two failed test:
\(\displaystyle{P}-{V}{a}{l}{u}{e}\ =\ {P}{\left({Z}\ {<}\ -{Z}_{{{s}{t}{a}{t}}}\right)}\ +\ {P}{\left({Z}\ {>}\ {Z}_{{{s}{t}{a}{t}}}\right)}\)
\(\displaystyle={2}\times\ {P}{\left({Z}{<}-{1.3429}\right)}={2}\times\ {0.0897}={0.1794}\)
p-value \(\displaystyle=\ {0.1794}\)
\(\displaystyle\alpha\ =\ {0.05}\)
As P-Value i.e. is greater than Level of significance i.e \(\displaystyle{\left({P}-{v}{a}{l}{u}{e}:{0.1794}{>}{0.01}\right.}\):Level of significance), Fail to Reject Null Hypothesis
There is not sufficient evidence to conclude that there is a significant difference in home ownership rates in the two groups of immigrants.

0
 
Best answer

expert advice

Have a similar question?
We can deal with it in 3 hours

Relevant Questions

asked 2021-02-09

A two-sample inference deals with dependent and independent inferences. In a two-sample hypothesis testing problem, underlying parameters of two different populations are compared. In a longitudinal (or follow-up) study, the same group of people is followed over time. Two samples are said to be paired when each data point in the first sample is matched and related to a unique data point in the second sample.
This problem demonstrates inference from two dependent (follow-up) samples using the data from the hypothetical study of new cases of tuberculosis (TB) before and after the vaccination was done in several geographical areas in a country in sub-Saharan Africa. Conclusion about the null hypothesis is to note the difference between samples.
The problem that demonstrates inference from two dependent samples uses hypothetical data from the TB vaccinations and the number of new cases before and after vaccination. \(\begin{array}{|c|c|} \hline Geographical\ regions & Before\ vaccination & After\ vaccination\\ \hline 1 & 85 & 11\\ \hline 2 & 77 & 5\\ \hline 3 & 110 & 14\\ \hline 4 & 65 & 12\\ \hline 5 & 81 & 10\\\hline 6 & 70 & 7\\ \hline 7 & 74 & 8\\ \hline 8 & 84 & 11\\ \hline 9 & 90 & 9\\ \hline 10 & 95 & 8\\ \hline \end{array}\)
Using the Minitab statistical analysis program to enter the data and perform the analysis, complete the following: Construct a one-sided \(\displaystyle{95}\%\) confidence interval for the true difference in population means. Test the null hypothesis that the population means are identical at the 0.05 level of significance.

asked 2021-01-28
Indicate true or false for the following statements. If false, specify what change will make the statement true.
a) In the two-sample t test, the number of degrees of freedom for the test statistic increases as sample sizes increase.
b) When the means of two independent samples are used to to compare two population means, we are dealing with dependent (paired) samples.
c) The \(\displaystyle{x}^{{{2}}}\) distribution is used for making inferences about two population variances.
d) The standard normal (z) score may be used for inferences concerning population proportions.
e) The F distribution is symmetric and has a mean of 0.
f) The pooled variance estimate is used when comparing means of two populations using independent samples.
g) It is not necessary to have equal sample sizes for the paired t test.
asked 2021-01-06
Inference about cause and effect but can't apply those inferences to population of interest. Which of the following best describes the statement above? Give full answer for your choice i. designed experiment in which experimental units are randomly sampled from the population of interest ii. designed experiment using available experimental units iii. observational study in which samples are randomly selected from preexisting distinct groups iv. observational study using nonrandom sample
asked 2021-01-10
Effect of alcoholic parents A study1 compared personality characteristics between 49 children of alcoholics and a control group of 49 children of nonalcoholics who were matched on age and gender. On a measure of well being, the 49 children of alcoholics had a mean of \(\displaystyle{26.1}{\left({s}={7.2}\right)}\) and the 49 subjects in the control group had a mean of \(\displaystyle{\left[{28.8}{\left({s}={6.4}\right)}\right]}\). The difference scores between the matched subjects from the two groups had a mean of \(\displaystyle{2.7}{\left({s}={9.7}\right)}\).
a. Are the groups to be compared independent samples or depentend samples? Why?
b. Show all speps of a test equality of the two population means for a two-sided alternative hypotesis. Report the P-value and interpret.
c. What assumptions must you make the inference in part b to be valid?
...