North Carolina State University posts the grade distribution for its courses online. Students in one section of English 210 in the Fall 2008 semester received 33% A's, 24% B's, 18% C's, 16% D's, and 9% F's.

A.) Using A=4, B=3, C=2, D=1, and F=0, take X to be the grade of a randomly chose English 210 student. Use the definition of mean, and standard deviation for discrete random variables to find the mean and standard deviation of grades in this course.

B.) English 210 is a large course. We can take the grade of an SRS of 50 students to be independent of each other. If x̅ is the average of these 50 grades, what are the mean and standard deviation of x?

C.) What is the probability P(X≥3) that a randomly chosen English 210 students gets a B or better? What is the approximate probability P(x̅ ≥3) that the grade point average for 50 randomly chosen English 210 students is a B or better?

D.) Give the 95% confidence interval of μ

A researcher would like to know whether there is a significant relationship between Verbal skills and Math skills in population of high school students. A sample of n = 200 students is randomly selected and each student is given a standardized Verbal skills test and a standardized Math skills test.

Based on the test results, students are classified as High or Low in Verbal skills and Math skills.

The results are summarized in the following frequency distribution table (i.e., the numbers represent the frequency count of students in each category):

Based on these results, can the researcher conclude that there is a significant

relationship between Verbal skills and Math skills? Test at the .05 level of significance.

For full credit, your answer must include:

         - hypotheses

         - computed Chi² test for Independence (show all computational steps)

         - computed phi-coefficient to measure the strength of the relationship

         - df and the critical Chi²value for p < .05

         - decision about H₀ and conclusion in the APA reporting format

Listed below are student evaluation ratings of​ courses, where a rating of 5 is for​ "excellent." The ratings were obtained at one university in a state. Construct a confidence interval using a

99% confidence level. What does the confidence interval tell about the population of all college students in the​ state?

4.0, 3.2, 4.2, 4.9, 3.0, 4.4, 3.8, 4.9, 4.5, 4.1, 4.1, 4.0, 3.4, 4.2, 3.9

What is the confidence interval for the population mean μ​?

___< μ​<___. (Round to two decimal places as needed.)

What does the confidence interval tell about the population of all college students in the​ state? Select the correct choice below​ and, if​ necessary, fill in the answer​box(es) to complete your choice.

A.We are 99​% confident that the interval from ____ to ____ actually contains the true mean evaluation rating.

​(Round to one decimal place as​ needed.)

B. The results tell nothing about the population of all college students in the​ state, since the sample is from only one university.

C.We are confident that 99​% of all students gave evaluation ratings between ___ and ___.

The distribution of the amount of money spent by students on textbooks in a semester is approximately normal in shape with a mean of 349 and a standard deviation of 24. According to the standard deviation rule, approximately 95% of the students spent between _____$ and _____$ on textbooks in a semester.

Question 12

Type numbers in the boxes.

1 points

The distribution of IQ (Intelligence Quotient) is approximately normal in shape with a mean of 100 and a standard deviation of 16. According to the standard deviation rule, ______% of people have an IQ between 52 and 148. Do not round.

Question 13

Type numbers in the boxes.

10 points

The distribution of IQ (Intelligence Quotient) is approximately normal in shape with a mean of 100 and a standard deviation of 13. According to the standard deviation rule, only _____% of people have an IQ over 139.

Question 14

Type numbers in the boxes.

10 points

The distribution of the amount of money spent by students on textbooks in a semester is approximately normal in shape with a mean of: μ= 310 and a standard deviation of: σ= 36.

According to the standard deviation rule, almost 2.5% of the students spent more than what amount of money on textbooks in a semester? _____

You are a nursing student at the XYZ College. It has a 50 percent acceptance rate (half the applicants do not get in). XYZ is a public college. XYZ has decided to implement an affirmative action policy. The college has few students over the age of 50. To encourage more students of that age, every student 50 or older will receive a bonus point. A student's admission is dependent on having 11 points. One earns points for a GPA above a certain score, ACT/SAT score above a certain number, having a letter of recommendation, etc. XYZ also lacks LGBT students, Muslim, and African-American students and is considering offering a bonus point for any student fitting those categories. What is the key moral conflict for XYZ? What social values should XYZ promote here? What diverse populations are involved here, and what are their interests? Do you think XYZ's social action is the correct solution to lack of diversity? Why or why not? Factor the ethics of egoism and utilitarianism into your answer.

A study was designed to compare the attitudes of two groups of nursing students towards computers. Group 1 had previously taken a statistical methods course that involved significant computer interaction. Group 2 had taken a statistic methods course that did not use computers. The students' attitudes were measured by administering the Computer Anxiety Rating Scale (CARS). A random sample of 10 nursing students from Group 1 resulted in a mean score of 45.3 with a standard deviation of 4.5. A random sample of 17 nursing students from Group 2 resulted in a mean score of 55.8 with a standard deviation of 6.9. Can you conclude that the mean score for Group 1 is significantly lower than the mean score for Group 2? Let μ1 represent the mean score for Group 1 and μ2 represent the mean score for Group 2. Use a significance level of α=0.1 for the test. Assume that the population variances are equal and that the two populations are normally distributed. Step 2 of 4 : Compute the value of the t test statistic. Round your answer to three decimal places

We selected a random sample of 100 StatCrunchU students, 67 females and 33 males, and analyzed their responses to the question, "What is the total amount (in dollars) of credit card debt you have accrued to date?"

With more than 30 in each random and independent sample, conditions are met for modeling the distribution of differences in sample means using a T-model. Therefore, we will proceed with finding a confidence interval to estimate the gender difference in credit card debt for StatCrunchU students.

Summary statistics for CC Debt:
Group by: Gender

Use StatCrunch to find the 95% confidence interval estimating the difference µ1 – µ2, where µ1 is the mean credit card debt for all female StatCrunchU students and µ2 is the mean credit card debt for all male StatCrunchU students.

Since the numbers are dollars, round to two decimal places when you enter your answer.

What is the lower limit on the confidence interval?

What is the upper limit on the confidence interval?

Suppose the correlation between first year GPA and second year GPA is 0.7. Assuming a close to linear relationship between GPAs in first year and in second year, what is the approximate average z-score in second year of students who had a z-score of 1.5 in their first-year GPA?

What is the average first-year z-score of students who have a z-score of 1.5 in their second-year GPA?

It seems that, on average, students who do well in first year do better than average in second year but not quite as well as they did in first year. And students who do better than average in second year did, on average, better than average in first year but not quite as well as they did in second year. Whichever way you go, from first year to second year, or from second year to first year, it looks like the grades are getting closer to the average.

Is this a contradiction? Is there an explanation for it? If you need a diagram to help explain it, go ahead a draw one

At the beginning of the Summer 2018 semester, a sample of 266 World Campus students were surveyed and asked if they were a first-generation college student. In the sample of 266, 139 said that they were first generation college students. We want to construct a 90% confidence interval to estimate the proportion of all World Campus students who are first generation students. A. In StatKey, construct a bootstrap distribution and use the percentile method to find the 90% confidence interval using the data given. Include a screenshot of your distribution here and clearly identify your confidence interval

.B. Use StatKey or Minitab Express to construct a z distribution to identify the z* multiplier for a 90% confidence interval. Include a screenshot of your distribution here and clearly identify your z* multiplier.

C. Use the formula from the online notes to construct the 90% confidence interval: sample statistic±z^* (standard error). You can use the standard error from the distribution you constructed in part A and the z* multiplier that you found in part B.

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=0.05 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.

Score on first SAT 470 560 430 590 490 410 460

Score on second SAT 520 620 450 610 530 460 500

Step 2 of 5 : Find the value of the standard deviation of the paired differences. Round your answer to one decimal place.