Question 1

Suppose you are comparing the mean test scores of students from two different universities. You collect a random sample of 40 students from each university. Which of the following is the most appropriate null hypothesis for this comparison?

Accepted Answer

$$H_0$$: \$$mu_1$$ = \$$mu_2$$

Question 2

You are comparing the average price per unit of two different brands of breakfast cereal. You collect 35 samples from each brand. Which statistical test should you use to compare the means, assuming the data is approximately normally distributed and variances are equal?

Accepted Answer

Two-sample t-test (pooled variance)

Question 3

When comparing two populations, why is it important to ensure that each sample is at least at the interval level of measurement?

Accepted Answer

Because interval data allows for meaningful calculation of differences and averages

Question 4

You are asked to calculate the 95% confidence interval for the difference in means between two independent samples. Which formula should you use?

Accepted Answer

$$ (\bar{x}_1 - \bar{x}_2) \pm t^* \sqrt{ \frac{s_1$^2}{n_1$} + \frac{s_2$^2}{n_2$} } $$

Question 5

A student wants to compare the average number of text messages sent per day by males and females. Which of the following best describes a potential source of error in their study?

Accepted Answer

Selection bias if the samples are not randomly chosen from each population

Question 6

If you are testing the claim that the mean price per unit of organic produce is higher than that of non-organic produce, which type of test should you use?

Accepted Answer

One-tailed (right) two-sample t-test

Question 7

You collect two samples of size 30 from two populations and calculate the following sample means and standard deviations: $$\bar{x}_1 = 50$$, $$s_1 = 5$, $$\bar{x}_2 = 47$$, s_2$ = 6. $$What is the value of the test statistic for a two-sample t-test (assuming equal variances)?

Accepted Answer

$$ t = \frac{50 - 47}{\sqrt{\frac{5^2$}{30} + \frac{6^2$}{30}}} $$

Question 8

Which of the following best describes the purpose of using randomization in selecting your samples?

Accepted Answer

To reduce bias and ensure that the sample is representative of the population

Question 9

You are comparing the mean number of hours studied per week by students on the east coast and west coast. After conducting your hypothesis test, you fail to reject the null hypothesis at the 5% significance level. What is the most appropriate conclusion?

Accepted Answer

There is not enough evidence to conclude a difference in mean study hours between the two coasts

Question 10

Which of the following is NOT a required component when reporting the results of a two-sample comparison project?

Accepted Answer

A table of the raw data for each sample

Question 11

If you are asked to construct a 99% confidence interval for the difference in means, what is the effect of increasing the confidence level from 95% to 99%?

Accepted Answer

The confidence interval becomes wider

Question 12

A student uses Excel to calculate the mean, median, mode, variance, and standard deviation for two samples. What is the primary purpose of these descriptive statistics in the context of comparing populations?

Accepted Answer

To summarize and compare the central tendency and variability of the two samples

Question 13

You are comparing the mean caffeine content in two brands of energy drinks. Your 95% confidence interval for the difference in means is $$(-2.5, 1.0). $$What does this interval suggest?

Accepted Answer

There is no statistically significant difference in mean caffeine content at the 5% level

Question 14

Which of the following best describes a histogram's role in comparing two samples?

Accepted Answer

It visually displays the shape and spread of each sample's distribution

Question 15

A researcher wants to compare the mean number of goals scored per game by two soccer teams. The sample sizes are 25 and 30, and the data is not normally distributed. Which approach is most appropriate?

Accepted Answer

Use a non-parametric test such as the Mann-Whitney U test

Question 16

When calculating the test statistic for a two-sample t-test, which of the following assumptions is NOT required?

Accepted Answer

The two samples have the same sample mean

Question 17

You are comparing the mean price per unit of two different products. Your sample means are $$\bar{x}_1 = 10$$ and $$\bar{x}_2 = 12$$, with standard errors of $$SE_1 = 1$ and SE_2$ = 1.5. $$What is the 90% confidence interval for the difference in means? (Use $$z^* = 1.645$$ for 90% confidence.)

Accepted Answer

$$ (10 - 12) \pm 1.645 	imes \sqrt{1^2$ + 1.5^2$} $$

Question 18

A student claims that the mean number of hours spent on homework per week is higher for science majors than for arts majors. Which of the following is the correct alternative hypothesis?

Accepted Answer

$$H_A: \mu_{science} \u003e \mu_{arts}$$

Question 19

Which of the following is a valid reason for using a two-tailed test instead of a one-tailed test when comparing two population means?

Accepted Answer

You want to detect any difference, regardless of direction

Question 20

In a two-sample comparison, which of the following would be a valid reason to discuss possible sources of error in your conclusion?

Accepted Answer

To acknowledge limitations such as sampling bias or measurement error

Comparing Populations: Statistical Analysis Project Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards