Question

In: Statistics and Probability

The following data set represents the final grades assigned in a statistics course. The grades are...

The following data set represents the final grades assigned in a statistics course. The grades are as followed, 60, 50, 85, 85, 85, 90, 100, 70, 83, 92, 68, 70, 88, 88, 85, 90, 20, 100, 90, 80, 77

1. Professor Williamson believes that the average grade she would assign would be an 85. Is she correct?

2. Determine an appropriate alpha level for the given data set and justify your reason

3. Create your null and alternate hypothesis

4. Perform a hypothesis test from the sample data

5. What is your t-value?

6. What is your critical T-value?

7. What is your estimated P-value or exact P-value?

8. Draw a normal curve of distribution that depicts your critical t-value, t-value and your P-value. Shade the graph where appropriate.

9. What is the general rule for all hypothesis testing when comparing p-values to alpha values?

10. Determine the conclusion of your data set using statistical language.

11. interpret your results of the data set based on the content of the question.

12. According to the Central limit theorem, the larger your sample size gets, something will happen to your data set. How does this affect hypothesis testing? Does this affect any type I or type II errors that could occur?

13. According to your results from this question, what conclusions can you make about the sample mean and Professor Williamson’s average?

Expert Solution

orchestra answered 1 year ago

A set of final examination grades in an introductory statistics course is normally distributed, with a...

A set of final examination grades in an introductory statistics course is normally distributed, with a mean of 7 and a standard deviation of 9. What is the probability that a student scored between 66 and 99?

A set of final examination grades in an introductory statistics course was found to be normally...

A set of final examination grades in an introductory statistics course was found to be normally distributed with a mean of 73 and a standard deviation of 8. What is the probability of getting a grade of 79 or less? What percentage of students scored between 61 and 81? What is the probability of getting a grade no higher than 72 (less than 72) on this exam?

A set of final exam grades in ST2500 course is normally distributed with mean 70 and...

A set of final exam grades in ST2500 course is normally distributed with mean 70 and standard deviation of 8. (a) What is the probability of getting a grade of A(greater or equal 80) on this exam? (4) (b) What is the probability of that a student scored between 65 and 79? (4) (c) The probability is 10% that a student taking the exam scores higher than what grade?

Two different professors teach an introductory statistics course. The table shows the distribution of final grades...

Two different professors teach an introductory statistics course. The table shows the distribution of final grades they reported. We wonder whether one of these professors is an "easier" grader. Answer parts a) and b) below. Prof. Alpha Prof. Beta A 5 10 B 12 12 C 15 8 Below C 13 3 a) Find the expected counts for each cell in this table. (Round to two decimal places as needed.) Prof. Alpha Prof. Beta A (blank) (blank) B (blank)...

The numerical course grades in a statistics course can be approximated by a normal model with...

The numerical course grades in a statistics course can be approximated by a normal model with a mean of 70 and a standard deviation of 10. The professor must convert the numerical grades to letter grades. She decides that she wants 10% A's, 30% B's, 40% C's, 15% D's, and 5% F's. a. What is the cutoff for an A grade? (Use 2 decimal places.) (Draw a picture!.) a. What is the cutoff for an B grade? (Use 2 decimal...

A statistics teacher believes that the final exam grades for her business statistics class have a...

A statistics teacher believes that the final exam grades for her business statistics class have a normal distribution with a mean of 82 and a standard deviation of 8. (1)Find the score which separates the top 10% of the scores from the lowest 90% of the scores. (2) The teacher plans to give all students who score in the top 10% of scores an A. Will a student who scored a 90 on the exam receive an A? Explain. (3)...

Suppose that the final grades in a stats course are approximately Normally distributed, with an average...

Suppose that the final grades in a stats course are approximately Normally distributed, with an average grade of 83 and a SD of 5. A student is randomly selected. a.) what is the probability that the selected student received an A (at least 90)? b.) the students know that their final grade is at the 81st percentile. Show whether or not that students grade is an A. c.) if the students final grade is a least a B-, what is...

An instructor hypothesizes that the variance of the final exam grades in her statistics class is...

An instructor hypothesizes that the variance of the final exam grades in her statistics class is larger for male students than it is for female students. The data from the final exam for the last semester are as shown. Is there enough evidence to support her claim, using a .01 level of significance? Males females n1=16 s1-4.2 n2=18 s2=2.3 claim ………………………………................ ________________________ null hypothesis…………………………………. ________________________ alternative hypothesis………………………….. ________________________ Calculator Screen Name……………………… ________________________ test statistic ………………………… ________________________ pvalue/alpha comparison………………………. ________________________...

A large group of students took a test in Statistics and the final grades have a...

A large group of students took a test in Statistics and the final grades have a mean of 70 and a standard deviation of 10. If we can approximate the distribution of these grades by a normal distribution, what percent of the students a) scored between 50 and 90? b) scored higher than 90? c) should pass the test (grades≥50) d)non of the above d) should fail the test (grades<50)?

A sample of 10 students was selected from a large statistics course. The grades of the...

A sample of 10 students was selected from a large statistics course. The grades of the 10 students on their test are shown below: 94 61 96 66 92 68 75 85 84 78 3a. Create a histogram, with the first class being 60-69. (3 pts) 3b. Calculate the following for the above data. Please only report the results. (8 pts) Mean = _____ Median = _____ Mode = _____ Range = ____ 3c. Calculate the standard deviation for the...