Indicate whether the given event is independent or not. Describe briefly.

c) The scores you receive on the first midterm, second midterm, and final exam of a course.

A professor would like to conduct a regression analysis to determine whether a student’s final exam score in her class can be predicted from the student’s midterm score. She records the midterm and final exam scores of a sample of students in her class. The midterm scores have a mean of 71.0 and a standard deviation of 9.4. The final exam scores have a mean of 66.2 and a standard deviation of 10.3. The correlation between midterm and final exam scores is calculated to be 0.84. What is the predicted increase in final exam score when a student’s midterm score increases by one?

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What is the benefit of reducing barriers to international trade?

Many students graduate from college deeply in debt from student loans, credit card debts, and so on. A sociologist took a random sample of 401 single persons, classified them by gender, and asked, Would you think about getting married to someone who owed $$ 25,000 or more? The following table displays the survey's findings. $$ $$ \begin{array}{lccc} \hline & \text { Yes } & \text { No } & \text { Uncertain } \\ \hline \text { Women } & 125 & 59 & 21 \\ \text { Men } & 101 & 79 & 16 \\ \hline \end{array} $$ $$ Check the relationship between gender and response at a $1 \%$ level of significance. $$

Choose the correct answer.

(a) To, (b) Too many students graduate from college heavily in debt.

A university employment office wants to compare the time taken by graduates with three different majors to find their first full-time job after graduation. The following table lists the time (in days) taken to find their first full-time job after graduation for a random sample of eight business majors, seven computer science majors, and six engineering majors who graduated in May 2009.

Business	Computer Science	Engineering
136	156	126
162	113	151
135	124	163
180	128	146
148	144	178
127	147	134
176	120
144

At the $5 \%$ significance level, can you conclude that the mean time taken to find their first full-time job for all May 2009 graduates in these fields is the same?

The president of a university claims that the mean time spent partying by all students at this university is not more than 7 hours per week. It was discovered through a random sample of 40 students from this university that they partied for an average of $9.50$ per hour the week before, with a standard deviation of $2.3$ per hour. Check the validity of the president's allegation at a $2.5% level of significance. Clearly state your conclusion.

A study claims that all adults spend an average of 14 hours or more on chores during a weekend. A researcher wanted to check if this claim is true. This researcher's random sample of 200 adults revealed that these adults put in an average of $14.65$ per hour on housework over the course of a weekend. The $3.00$ hour population standard deviation is well known. a. The alternative hypothesis is that all adults spend more than 14 hours on housework on the weekends. Calculate the $p$-value for the hypothesis test with this alternative hypothesis. At $\alpha=.01$, will you reject the null hypothesis? b. Test the hypothesis of part a using the critical-value approach and $\alpha=.01$.

A statistics instructor wanted to see if student participation in review preparation methods led to higher examination scores. Five students were randomly selected and placed in each test group for a three-week unit on statistical inference. Everyone took the same examination at the end of the unit, and the resulting scores are shown. Is there sufficient evidence at $\alpha=0.05$ to conclude an interaction between the two factors? Is there sufficient evidence to conclude a difference in mean scores based on formula delivery system? Is there sufficient evidence to conclude a difference in mean scores based on the review organization technique?

	Formulas provided	Student-made formula cards
Student-led review	89,76,80,90,75	94,86,80,79,82
Instructor-led review	75,80,68,65,79	88,78,85,65,72

If the null hypothesis is rejected, use Scheffe's test when the sample sizes are unequal to test the differences between the means and use the Tukey test when the sample sizes are equal. For these exercises, perform these steps. Assume the assumptions have been met.

a. State the hypotheses and identify the claim. b. Find the critical value(s). c. Compute the test value. d. Make the decision. e. Summarize the results.

In a sample of 50 men, 44 said that they had less leisure time today than they had 10 years ago. In a random sample of 50 women, 48 women said that they had less leisure time than they had 10 years ago. At $\alpha=0.10$, is there a difference in the proportions? Find the $90 \%$ confidence interval for the difference of the two proportions. Does the confidence interval contain 0 ? Give a reason why this information would be of interest to a researcher. Perform these steps.

a. State the hypotheses and identify the claim. b. Find the critical value(s). c. Compute the test value. d. Make the decision. e. Summarize the results.

Use the traditional method of hypothesis testing unless otherwise specified.

Execute these steps.

a. State the hypotheses and identify the claim. b. Find the critical value(s). c. Compute the test value. d. Make the decision. e. Summarize the results.

Employ the traditional method of hypothesis testing unless otherwise specified.

The percentages of adults 25 years of age and older who have completed 4 or more years of college are $23.6 \%$ for females and $27.8 \%$ for males. A random sample of women and men who were 25 years old or older was surveyed with these results. Estimate the true difference in proportions with $95 \%$ confidence, and compare your interval with the Almanac statistics.

	Women	Men
Sample size	350	400
No. who completed 4 or more years	100	115

Perform each of the following steps.

a. State the hypotheses and identify the claim. b. Find the critical value(s). c. Find the test value. d. Make the decision. e. Summarize the results.

Use the traditional method of hypothesis testing unless otherwise specified. This table lists the numbers of officers and enlisted personnel for women in the military. At $\alpha=0.05$, is there sufficient evidence to conclude that a relationship exists between rank and branch of the Armed Forces?

	Officers	Enlisted
Army	10,791	62,491
Navy	7,816	42,750
Marine Corps	932	9,525
Air Force	11,819	54,344

Assume that all variables are normally or approximately normally distributed.
Use the traditional method of hypothesis testing unless the $\mathrm{P}$-value method is specified by your instructor. Assume the variances are unequal.
Hours Spent Watching Television According to Nielsen Media Research, children (ages $2-11$) spend an average of $21$ hours $30$ minutes watching television per week while teens (ages $12-17$) spend an average of $20$ hours $40$ minutes. Based on the sample statistics shown, is there sufficient evidence to conclude a difference in average television watching times between the two groups? Use $\alpha=0.01$.

$$\begin{array}{lll} & \text { Children } & \text { Teens } \\ \hline \text { Sample mean } & 22.45 & 18.50 \\ \text { Sample variance } & 16.4 & 18.2 \\ \text { Sample size } & 15 & 15 \end{array}$$

c. Compute the test value.