A professor has kept track of test scores for students who have attended every class and for students who have missed one or more classes. below are scores collected so far.

perfect: 80,86,85,84,81,92,77,87,82,90,79,82,72,88,82

missed 1+:61,80,65,64,74,78,62,73,58,72,67,71,70,71,66

1. Evaluate the assumptions of normality and homoscedasticity

2. conduct a statistical test to assess if exam scores are different between perfect attenders and those who have missed class

3. What is the meaning of the 95% confidence interval given from the R code. What does the 95% CI explain compared to the hypothesis test and how does the 95% CI relate to the test statistic and p value

Q1. Jamie wants to forecast the number of students who will enroll in operations management next semester in order to determine how many sections to schedule. He has accumulated the following enrollment data for the past six semesters:

a (2 pts). Compute a three-semester moving average forecast for semesters 4 through 7 (Model a) (Use two decimals).

1. A large insurance company wants to determine whether the proportion of male policyholders who would not submit auto insurance claims of under $500 is the same as the proportion of female policyholders who do not submit claims of under $500. A random sample of 400 male policyholders produced 272 who had not submitted claims of under $500, whereas a random sample of 300 female policyholders produced 183 who had not submitted claims of under $500

a) Construct a 90% confidence interval for the difference between the proportions of males and of females who had not submitted auto insurance claims of under $500.

b) Find the p-value of the appropriate test.

In a random sample of 10 LAS students, the sample mean time spent studying during a particular week was 15.7 hours with sample standard deviation 3.1 hours. In a random sample of 8 Engineering students, the sample mean time studying during the same week was 20.2 hours per month with sample standard deviation 4.4 hours. Assume that the two populations are normally distributed.

a) Assume that the two population variances are equal. Construct a 95% confidence interval for the difference between the overall average times Engineering and LAS students spent studying during this week.

b) Since the larger sample variance is more than twice as big as the smaller one, the assumption of equal variances is questionable here. Construct a 95% confidence interval for the difference between the overall average times Engineering and LAS students spent studying during this week without assuming that the two population variances are equal. Use Welch’s T.

1. Minorities in Higher Education

You are a social psychologist interested in the adjustment of international students who go to school at American universities. You decide to examine whether there are differences in scores on the Acceptability by Others Scale (AOS). The AOS is a scale that ranges from 1 to 20 (1 = feeling completely isolated – 20 feeling completely accepted) that measures acceptance within the college community. You collect scores on the AOS from a sample of international students (Int) at a small college in the United States and another sample of United States (U.S.) citizens attending the same college. The data is provided below. Conduct a two-tailed independent-samples t-test by hand using an alpha level of .05 to determine whether there are differences in AOS scores between the two samples. Record your answers below.

1. Step #1: A priori expectations
   1. Question of interest:

2. Prediction:

2. Step #2: Set up hypotheses
   1. H₀:

2. H₁:

3. Step #3: Set criteria for decision
   1. t_cv (critical value for rejecting the null hypothesis)

2. Decision rule for when to reject the null hypothesis:

4. Step #4: Collect data/ compute statistic

5. 
   Step #5: Report results in standard format – Must include test statistic , degrees of freedom, p-value , 95% confidence interval (95% C.I.) and conclusion (reject or fail to reject H₀)

​​​​​​​6. Step #6: Interpret the results of the statistical test in terms of the research question

1. Minorities in Higher Education

You are a social psychologist interested in the adjustment of international students who go to school at American universities. You decide to examine whether there are differences in scores on the Acceptability by Others Scale (AOS). The AOS is a scale that ranges from 1 to 20 (1 = feeling completely isolated – 20 feeling completely accepted) that measures acceptance within the college community. You collect scores on the AOS from a sample of international students (Int) at a small college in the United States and another sample of United States (U.S.) citizens attending the same college. The data is provided below. Conduct a two-tailed independent-samples t-test by hand using an alpha level of .05 to determine whether there are differences in AOS scores between the two samples. Record your answers below.

1. Step #1: A priori expectations
   1. Question of interest:

2. Prediction:

2. Step #2: Set up hypotheses
   1. H₀:

2. H₁:

3. Step #3: Set criteria for decision
   1. t_cv (critical value for rejecting the null hypothesis)

2. Decision rule for when to reject the null hypothesis:

4. Step #4: Collect data/ compute statistic

5. 
   Step #5: Report results in standard format – Must include test statistic , degrees of freedom, p-value , 95% confidence interval (95% C.I.) and conclusion (reject or fail to reject H₀)

​​​​​​​6. Step #6: Interpret the results of the statistical test in terms of the research question

(Survey from 9.41: In a survey of 446 students, it was found that 50% of the sampled students lived on campus and 50% lived off campus.)

In the same survey used in 9.41, 88% of the sampled students were right-handed.

a. The proportion of all people who are right-handed is said to be 0.88. Tell the value of standardized sample proportion z, if we want to test whether the proportion of all students who are right- handed could be 0.88.

b. If we sketch a normal curve for the distribution of sample proportion (centered at 0.88), what portion should be shaded to indicate the area represented by the P-value for testing against the alternative that population proportion is less than 0.88? [Please see the three graphs on p. 000 for examples of P-value as a shaded area.]

c. What portion of the standard normal (z) curve should be shaded to indicate the area represented by the P-value for testing against the alternative that the population proportion is less than 0.88? What does the P-value equal in this case?

d. What portion of the normal curve for the distribution of sample proportion (again, centered at 0.88) should be shaded to indicate the area represented by the P-value for testing against the (two-sided) alternative that population proportion does not equal 0.88? What does the P-value equal in this case?

e. What portion of the normal curve for the distribution of standardized sample proportion z should be shaded to indicate the area represented by the P-value for testing against the (two-sided) alternative that population proportion does not equal 0.88?

f. Will the null hypothesis be rejected against either the one-sided or two-sided alternative? Explain.

An SAT prep course claims to improve the test score of students. The table below shows the scores for seven students the first two times they took the verbal SAT. Before taking the SAT for the second time, each student took a course to try to improve his or her verbal SAT scores. Do these results support the claim that the SAT prep course improves the students' verbal SAT scores?

Let d=(verbal SAT scores prior to taking the prep course)−(verbal SAT scores after taking the prep course)d=(verbal SAT scores prior to taking the prep course)−(verbal SAT scores after taking the prep course). Use a significance level of α=0.05α=0.05for the test. Assume that the verbal SAT scores are normally distributed for the population of students both before and after taking the SAT prep course.

Step 2 of 5:

Find the value of the standard deviation of the paired differences. Round your answer to one decimal place.

Step 3 of 5:

Compute the value of the test statistic. Round your answer to three decimal places.

Step 4 of 5:

Determine the decision rule for rejecting the null hypothesis H0H0. Round the numerical portion of your answer to three decimal places.

Step 5 of 5:

Make the decision for the hypothesis test.

An SAT prep course claims to improve the test score of students. The table below shows the scores for seven students the first two times they took the verbal SAT. Before taking the SAT for the second time, each student took a course to try to improve his or her verbal SAT scores. Do these results support the claim that the SAT prep course improves the students' verbal SAT scores?

Let d=(verbal SAT scores prior to taking the prep course)−(verbal SAT scores after taking the prep course)d=(verbal SAT scores prior to taking the prep course)−(verbal SAT scores after taking the prep course). Use a significance level of α=0.01 for the test. Assume that the verbal SAT scores are normally distributed for the population of students both before and after taking the SAT prep course.

Copy Data

Step 1 of 5:

State the null and alternative hypotheses for the test.

Step 2 of 5:

Find the value of the standard deviation of the paired differences. Round your answer to one decimal place.

Step 3 of 5:

Compute the value of the test statistic. Round your answer to three decimal places.

Step 4 of 5:

Determine the decision rule for rejecting the null hypothesis H0. Round the numerical portion of your answer to three decimal places.

Step 5 of 5:

Make the decision for the hypothesis test.

An SAT prep course claims to improve the test score of students. The table below shows the scores for seven students the first two times they took the verbal SAT. Before taking the SAT for the second time, each student took a course to try to improve his or her verbal SAT scores. Do these results support the claim that the SAT prep course improves the students' verbal SAT scores?

Let d=(verbal SAT scores prior to taking the prep course)−(verbal SAT scores after taking the prep course). Use a significance level of α=0.1 for the test. Assume that the verbal SAT scores are normally distributed for the population of students both before and after taking the SAT prep course.

Step 1: State the null and alternative hypotheses for the test.

Answer: Ho: Md = 0

Ha: Md < 0

Step 2: Find the value of the standard deviation of the paired differences. Round your answer to one decimal place.

Answer: Sd= 26.5

Step 3: Compute the value of the test statistic. Round your answer to three decimal places.

Answer: -4.992

Step 4: Determine the decision rule for rejecting the null hypothesis H0. Round the numerical portion of your answer to three decimal places.

Answer?????

Step 5: Make the decision for the hypothesis test.

Answer?????

Answer parts 4 and 5 please. Steps 1, 2, and 3 are correct.