Name: _______________________________________  Stat 215 – Summer 2019 Final #1 

Directions: Answer each question fully and to the best of your ability. Show all work and round answers to 4 decimal places.

 1. Use the following dataset to find the following statistics. x: 99, 136, 116, 175, 189, 2, 171, 24 

A. Find the sample standard deviation.

B. Give an interpretation of your calculated standard deviation. 

C. Find the skewness 

D. Give an interpretation of skewness

 E. What two features distinguish a histogram that follows the Normal Distribution?

 F. Find the value of the median

 G. Match each histogram to the boxplot that represents the same data set. a. ________ b. ________ c. ________ d. ________ 

2. Suppose that one word is to be selected at random from the sentence The girl put on her lovely pink hat. If X denotes the number of letters in the word that is selected. What is the value of E(X)? What is the value of Var(X)? 

3. Suppose that the measured voltage in a certain electric circuit has the normal distribution with mean 150 and variance 4. If three independent measurements of the voltage are made, what is the probability that all three measurements will lie between 146 and 148? 

4. Two different teaching procedures were used on two different groups of students. Each group contained 100 students of about the same ability. At the end of the term, an evaluating team assigned a letter grade to each student. The results were tabulated as follows: Grade Group A B C D F Total I 15 22 32 17 14 100 II 9 16 29 28 18 100 If we consider this data to be comprised of independent observations, test at the 5 percent significance level the hypothesis that the two teaching procedures are equally effective. 

5. The manager of a door-making company would like to estimate the amount of time it takes for a piece of wood to be moved, cut, and packaged at two different plants. At Plant A, the manager observed 21 pieces that processed with an average time of 14.2 minutes and standard deviation of 2.6 minutes. At the second plant, the manager observed 19 pieces with an average time of 13.1 minutes with a standard deviation of 1.9 minutes. 

a. Test whether there is a difference between mean process times of Plants A and B with an assumed α = 0.1. State your conclusion properly with context. 

b. What three assumptions are required to perform the above test?

 c. Using the above information and α = 0.1 significance level, test to see if the plants have different variability. State your conclusion properly with context. 

6. The distance between defects on a long wire is exponentially distributed with mean 14 mm. a. What is the probability that the distance between two defects is greater than 17 mm? b. Find the probability that the distance between two defects is between 11 and 20. 

7. A consumer group is interested in estimating the proportion of packages of ground beef sold at a particular store that have an actual fat content exceeding the fat content stated on the label. How many packages of ground beef should be tested to estimate this proportion to within 0.03 with 98% confidence?

 8. Let the number of chocolate chips in a chocolate chip cookie have a Poisson distribution. We want the probability that a cookie of this type contains at least one chocolate chips to be greater than 0.99. Find the smallest value of the mean that the distribution can take. 

 9. Do teachers find their work rewarding and satisfying? An article in Psychological Reports reported the results of a survey of a random sample of 395 elementary teachers and 266 high school teachers. Of the elementary school teachers, 224 said that they were very satisfied with their jobs, whereas 166 of the high school teachers were very satisfied with their work. a. Based on this data, is it reasonable to conclude that the proportion of very satisfied teachers is different for elementary teachers than it is for high school teachers? Please state conclusion properly with context. b. Construct and interpret a 95% Confidence Interval in the context of the above scenario. c. How do the results in Part a and b compare? Do the results contradict each other? 

10. In a certain factory, machines I, II, and III are all producing springs of the same length. Machines I, II, and III produce 1%, 5% and 3% defective springs, respectively. Of the total production of springs in the factory, Machine I produces 26%, Machine II produces 32%, and Machine III produces 42%. a. If one spring is selected at random from the total springs produced in a given day, what is the probability that it is defective? b. Given that the selected spring is defective, find the conditional probability that it was produced by Machine II. 

11. At a used-book sale, 100 books are adult books and 160 are children’s books. Seventy of the adult books are nonfiction while 100 of the children’s books are fiction. Assume a book is selected at random, what is the probability that the book is an adult book or a children’s nonfiction book?

 12. A federal job placement director claims that the average starting salary for nurses is $66,500. A sample of 10 nurses in Morgantown has a mean of $49,900 and a standard deviation of $5,000. Is there enough evidence to determine if Morgantown nurses make a smaller salary than the national average at 𝛼 = 0.05? 13. In a study of memory recall, 8 students from a large psychology class were selected at random and given 10 min to memorize a list of 20 nonsense words. Each was asked to list as many of the words as he or she could remember both 1 hour and 24 hours later, as shown in the following table: Subject 1 2 3 4 5 6 7 8 1 Hour 14 12 18 7 11 9 16 15 24 Hours 10 4 14 6 9 6 12 12 Is there evidence to suggest that the mean number of words recalled after 1 hour exceeds the mean recall after 24 hours by more than 3? Use a level .01 test. 

14. The probability distribution of x, the number of defective tires on a randomly selected automobile checked at a certain inspection station, is given in the following table: 𝑥 0 1 2 3 4 𝑝(𝑥) 0.5423 0.1607 0.0546 0.0414 0.2010

 a. Calculate the mean value of x. b. Calculate the standard deviation of x c. What is the probability that x exceeds its mean value? 

15. Suppose that 85 percent of the students at WVU live in student housing and 15 percent of students at WVU have alternative housing. If 1,776 students attending a career planning event represent a random sample from the student population, what is probability that the number of students with alternative housing will be fewer than 213? 

16. Liam is a little boy who is about to have his first Tee-Ball practice. Unfortunately, Liam isn’t very good, and the probability that he catches a ball is only 0.1. Let x be the number of tosses required until Liam catches a ball. 

a. What is the probability that it will take exactly two tosses for Liam to catch a ball? 

b. What is the probability that more than three tosses will be required? 

17. How is the power of the test related to the type II error? 

18. How can the power of a test be increased? 

19. What is considered a large sample?