News of your analytical prowess has spread throughout the area.Naturally, when the coaching staff of your teen's high school lacrosse team has a statistical question, they contact the best, you.The coaching staff wants to know if the average difference between the home team and their opponent is more than +2 points.Use the data below from 35 randomly chosen games to answer their question using = 0.01.The home team's scores are listed first.

12 - 6 7 - 5 10 - 4 5 - 6 9 - 8 7 - 5 7 - 2

8 - 6 8 - 2 8 - 4 7 - 1 8 - 5 6 - 4 13 - 5

10 - 4 5 - 8 9 - 6 6 - 5 5 - 4 10 - 6 7 - 10

14 - 10 7 - 2 6 - 5 6 - 5 7 - 6 8 - 7 8 - 3

9 - 8 8 - 6 10 - 4 10 - 9 6 - 7 8 - 1 8 - 5

Determine if assumptions have been met by asking

1 2 random sample?

2 Are samples independent?

3 are samples larger?

1.What is the name of the type of hypothesis test required here?

Is this a left-tailed, right-tailed, or two-tailed test?

2.State AND verify all assumptions required for this test.

3.State the null and alternate hypotheses for this test: (use correct symbols and format!)

Null hypothesis

Alternate hypothesis

4.Run the correct hypothesis test and provide the information below.Give the correct symbols AND numeric value of each of the following (Round answers to 3 decimal places).

Test Statistic

Critical value [HINT: this is NOTa ]

Degrees of Freedom

p-value

5.State your statistical decision (and justify it!) and interpret your decision within the context of the problem. What is your conclusion?

Part 2) Teacher Salaries (7 points)

A researcher claims that the mean of the salaries of elementary school teachers is greater than the mean of the salaries of secondary school teachers in a large school district. The mean of the salaries of a random sample of 46 elementary school teachers is $48,256, and the sample standard deviation is $3,912. The mean of the salaries of a random sample of 34 secondary school teachers is $45,633, and the sample standard deviation is $5,533. At= 0.05, can it be concluded that the mean of the salaries of the elementary school teachers is greater than the mean of the salaries of the secondary school teachers?

1.What is the name of the type of hypothesis test required here? Is this a left-tailed, right-tailed, or two-tailed test? State AND verify all assumptions required for this test.

2.State the null and alternate hypotheses for this test: (use correct symbols and format!)

Null hypothesis

Alternate hypothesis

3.Run the correct hypothesis test and provide the information below.Give the correct symbols AND numeric value of each of the following (round answers to 3 decimal places).

Test Statistic

Critical value(s)

Degrees of Freedom

p-value

4.State your statistical decision (and justify it!) and interpret your decision within the context of the problem. What is your conclusion?

5.Calculate the 95% confidence interval for the difference of the average salaries of elementary school teachers and secondary school teachers.Show your work or calculator functions!

6.Does your confidence interval support or contradict your conclusion from the hypothesis test you completed?Explain how you know.

Part 3) Interview Errors (3 points)

It has been found that many first-time interviewees commit errors that could very well affect the outcome of the interview. One major error many of them make is using their cell phones or texting during the interview! A researcher wanted to see if the proportion of male offenders differed from the proportion of female offenders. Out of 120 males, 72 reported using their cell phones during a job interview and 80 of 150 females did so. Is there a difference between the proportions of males and females who made this error at a job interview with 95% confidence (or = 0.05)? Use a 95% confidence interval and show your work or calculator function to receive full credit.