stat 200 midterm exam

Stat 200 6376 (2215) - MID TERM EXAM

Summer 2021

Professor: Jose R. Martinez Castillo

Name: James Shanique V.

Instructions:

· The quiz is worth 100 points total. Your score on the Exam will be posted in your assignment folder with comments.

· This Exam allows open book and open notes, and you may take as long as you like on it, provided that you submit the quiz no later than the due date posted in our course schedule of the syllabus. You may refer to your textbook, notes, and online classroom materials, but you may not consult anyone.

· You should show all of your work to receive full credit. If you do not show work, you may earn only partial or no credit.

· Please type your work in your copy of the quiz, or if you prefer, create a document containing your work. Scanned work is also acceptable. Be sure to include your name in the document. Review instructions for submitting your quiz in the Quizzes Module.

· If you have any questions, please contact me by e-mail ([email protected]).

Honor Statement: At the end of your quiz you must include the following dated statement with your name typed in lieu of a signature.  Without this signed statement you will receive a zero.

I have completed this quiz myself, working independently and not consulting anyone except the instructor. I have neither given nor received help on this quiz.

Name: James Shanique V.                                                          Date: June 19, 2021

1. The following are the ages of a group of tourists visiting The Library of Congress:

36, 38, 33, 44, 37, 37, 38, 34, 34, 36, 34, 40, 42, 41, 35, 48, 31, 33, 46, 47, 33, 36, 37, 37, 34, 39, 35, 37, 36, 39, 39

a) Construct the Histogram of the ages with a class width of 5 years.

b) Find the mean of the dataset.

c) Find the median of the dataset.

2. True or false - for the dataset: 13, 13, 15, 15, 16, 16, 16, 17, 18, 22

a) The maximum value of the dataset above is 22. If the analyst makes one mistake and record it as 2.2, then the mistake will change the mean and the median of the dataset. Show calculations.

b) If the variance of a dataset is zero, then all observations must also be zero.

c) The standard deviation of dataset cannot be negative.

d) The variance of a dataset is always positive.

e) The following graph have a negative correlation:

3. A shipment of thirteen smartphones contains three with cracked screens. If sold in a random order, what is the probability that the first ten sold have undamaged screen?

4. When you toss a fair six-faced die two times many outcomes can happen:

a) Determine the number of possible outcomes in the sample space. Explain your answer.

b) Calculate the probability that you get a number greater than 5 at the first toss. Show work and write the answer in the simplest fraction form.

c) Calculate the probability that the sum of the two tosses is at lest 7. Show work and write the answer in the simplest fraction form.

d) Calculate the probability that the sum of the two tosses is at least 7, given that you get a number greater than 2 in the first toss. Show work and write the answer in the simplest fraction form.

e) If event A is “Getting a number greater than 4 in the first toss”, and event B is “The sum of two tosses is at least 8”. Are event A and event B independent. Justify your answer.

5. The SAT Math scores for all seniors in a High Schools are normally distributed with population standard deviation of 200. If 100 seniors from the school are randomly selected, and their SAT Math scores have a sample mean of 650, determine:

1. What distribution will you use to determine the critical value for a confidence interval estimate of the mean SAT Math score for the seniors in the High School? Why?

2. Construct a 95% confidence interval estimate of the mean Math score for the seniors in the High School. Show work and round the answer to two decimal places.

6. There are sixteen shirts in your closet, eight blue and eight green. You randomly select one shirt to wear on Monday, and then a different one on Tuesday. You wear a blue shirt on Monday and a green shirt on Tuesday. Determine whether the scenario involves independent or dependent event. Find the probability.

7. You are setting the combination on a four-digit lock. You want the number 1234 but don´t care what order they are in. Find the number of possibilities.

8. Is a 90% confidence interval estimate of the mean SAT Math score wider than the 95% confidence interval estimate you got from part 2 in Problem 5)? Why? Note: you don´t have to actually construct the 90% confidence interval.

9. Assume the population is normally distributed. Given a sample size of 225, with sample mean of 750 and standard deviation of 30, we perform the following hypothesis test.

H0: μ = 745

Ha: μ ≠ 745

(a) Is this test for population proportion, mean or standard deviation? What distribution should you apply for the critical value?

(b) What is the test statistic? (Show work and round the answer to three decimal places)

(c) What is the p-value? (Show work and round the answer to two decimal places. If you use technology to find the P-value, you have to describe the steps).

10. Five hundred students took a chemistry test. You sampled 100 students to estimate the average score and the standard deviation. How many degrees of freedom were there in the estimation of the standard deviation? (Justify for full credit)

(a) 500 (b) 499 (c) 100 (d) 99

online applet on hackmath.net and excel (NORMINV)