# Identify the type of random sampling used in the study design. The researcher is interested compare the student's loan debt for the students who attend four-year public universities and four-year private universities. A random sample of 100 graduates of the public universities and 100 graduates of private universities are taken.

Question
Study design
Identify the type of random sampling used in the study design.
The researcher is interested compare the student's loan debt for the students who attend four-year public universities and four-year private universities. A random sample of 100 graduates of the public universities and 100 graduates of private universities are taken.

2020-10-28
Stratified random sampling:
In stratified sampling the entire population is divided into two or more separate groups based on certain characteristics based on subjects. These separate groups are termed as strata. Then for each group (stratum) the units are selected using the simple random sample.
Justification: The researcher is interested compare the student’s loan debt for two groups of students belonging to ‘four-year public universities, four-year private universities’. The entire population of the students is divided into two separate groups termed strata. For each group 100 graduates are selected using simple random sampling. Since the population is divided into groups and simple random sample is used for selecting the subjects for two groups, the study design used stratified random sample.
Hence, the type of random sampling used in the study design is stratified random sampling.

### Relevant Questions

A random sample of $$n_1 = 14$$ winter days in Denver gave a sample mean pollution index $$x_1 = 43$$.
Previous studies show that $$\sigma_1 = 19$$.
For Englewood (a suburb of Denver), a random sample of $$n_2 = 12$$ winter days gave a sample mean pollution index of $$x_2 = 37$$.
Previous studies show that $$\sigma_2 = 13$$.
Assume the pollution index is normally distributed in both Englewood and Denver.
(a) State the null and alternate hypotheses.
$$H_0:\mu_1=\mu_2.\mu_1>\mu_2$$
$$H_0:\mu_1<\mu_2.\mu_1=\mu_2$$
$$H_0:\mu_1=\mu_2.\mu_1<\mu_2$$
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The standard normal. We assume that both population distributions are approximately normal with known standard deviations.
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(Test the difference $$\mu_1 - \mu_2$$. Round your answer to two decimal places.) NKS (d) Find (or estimate) the P-value. (Round your answer to four decimal places.)
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At the $$\alpha = 0.01$$ level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
At the $$\alpha = 0.01$$ level, we reject the null hypothesis and conclude the data are statistically significant.
At the $$\alpha = 0.01$$ level, we fail to reject the null hypothesis and conclude the data are statistically significant.
At the $$\alpha = 0.01$$ level, we reject the null hypothesis and conclude the data are not statistically significant.
(f) Interpret your conclusion in the context of the application.
Reject the null hypothesis, there is insufficient evidence that there is a difference in mean pollution index for Englewood and Denver.
Reject the null hypothesis, there is sufficient evidence that there is a difference in mean pollution index for Englewood and Denver.
Fail to reject the null hypothesis, there is insufficient evidence that there is a difference in mean pollution index for Englewood and Denver.
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$$\mu_1 - \mu_2$$.
lower limit
upper limit
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Because the interval contains only positive numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is greater than that of Denver.
Because the interval contains both positive and negative numbers, this indicates that at the 99% confidence level, we can not say that the mean population pollution index for Englewood is different than that of Denver.
Because the interval contains both positive and negative numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is greater than that of Denver.
Because the interval contains only negative numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is less than that of Denver.
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