STAT 1342 Fall 2013 FINAL EXAM

NAME:______ID: ______

Instructions:Identify the best response from the answers for each question/subquestion. There are 26 questions and each question carries 4 points, Question 18 is bonus.

1-3.Here is a stem-leaf plot of the exam scores of 26 students. The scores range from 50 to 98.

STEM | LEAF

5 | 0

6 | 38

7 | 3678999

8 | 002333556689

95678

  1. The median of this distribution of exam scores is______.

(a)83(b) 82(c) 82.5(d) 87

  1. The textbook’s method for finding the third (upper) quartile Q3 leads to the value______.

(a)86(b) 82(c) 87(d) 87.5

  1. This distribution of sample scores is best described as ______

(a)symmetric about its mean

(b)skewed to the right (positively skewed)

(c)skewed to the left (negatively skewed)

4-7. In Professor Friedman’s economics course the correlationcoefficient between the students’ total score prior to the final examination and their final examination score is r=.6. The pre-exam totals for all students in the course have mean 280 and standard deviation 30. The final-exam have mean 75 and standard deviation 8(listed in the table below).

sample mean / sample standard dev.
Pre-exam (X) / 280 / 30
Final-exam (Y) / 75 / 8
  1. Professor Friedman wants to predict his students’ final-exam score from their pre-exam total. Determine the linear regression line.

(a)y=280+.6*x

(b)y=75+56*x

(c)y=119.8-.16*x

(d)y=30.2+.16*x

  1. Professor Friedman wants to predict Julie’s final-exam score from her pre-exam total, which is 300. Use the regression line to predict Julie’s final-exam score.

(a)71.8(b) 78.2(c) 80(d) 82.2

  1. We observe that Julie’s record is (300, 88), What is the residual for the observation?

(a) 9.8(b) 16.2(c) -9.8(d) 0

  1. How much of the variation has been determined by the linear regression.

(a)60%(b) 36%(c) 80%(d) unknown

8-9.In a big bag of M&M candy, 20% of candies are red covered, 30% are brown covered, 10% are green covered, 20% are yellow, and the rest are blue, shown as follows

Red / Brown / Green / Yellow / Blue
20% / 30% / 10% / 20% / ?
  1. What is the chance you get a blue one?

(a) 0.14(b) 0.25(c) 0.20(d)0.85

  1. What is the chance you get a candy that is not brown?

(a) 0.80(b) 0.85(c) 0.40(d)0.70

10-11. The National Longitudinal Study of Adolescent Health interviewed several thousands teens (grades 7 to 12). One question asked was “What do you think are the chances you will be married in the next ten years?” Here is a two-way table of the responses by gender.

Female / Male
Almost no chance / 119 / 103
Some chance, but probably not / 150 / 171
A 50-50 chance / 447 / 512
A good chance / 735 / 710
Almost certain / 1174 / 756
  1. The percent of teens who responded “almost certain” among female is about

(a) 33.6%(b) 39.6%(c) 44.7%(d)26.2%

  1. The percent of females among the respondent was

(a) about 46%(b) about 54%(c) about 86%(d) about 50%

12-15.Lay’s company claims that the weight of their certain potato chips bag is normally distributed with a mean of 42.5 grams and a standard deviation of 1 gram.

  1. What is the probability that you get a bag of chips between 41.5 and 43.5 grams?

(a).68(b).95(c) .997(d) .75

  1. Find the weight (in gram) of a bag of lay’s potato chips over which 5% of all the weights lies.

(a)43 (b) 50 (c) 44.15(d) 44.5

  1. We have a box with 12 random bags of potato chips, the mean and the standard deviation for the average weight (in gram) are______gram respectively.

(a)42.5, 1(b) 43, 1(c) 42.5,.33(d) 42.5, .29

  1. What is the probability that a box with 12 bags of potato chips has an average weight that is less than 42 grams?

(a).0427(b) .0625(c) .3085(d) .3462

16-18.Suppose that salaries of high school teachers in public schools in Michigan over the last year have a Normal distribution. A sample of 46 high school teachers was drawn for the analysis of their salaries, and the sample average salary is $50,200.

  1. If we want to construct confidence interval for the population average with 95% confidence if the population standard deviation σis specified as $3,000. What kind of confidence interval we should construct,

(a)one sample Z interval

(b)two sample Z interval

(c)one sample t interval

(d)one sample proportion interval

  1. How will you interpret these interval?

(a) The salary of 95% high school teachers in public schools in Michigan is in the interval.

(b)You are 95% sure that the average mean salary for all high school teachers in public schools in Michigan will lie in the interval.

(c) There is a 95% probability that the mean is in the interval.

(d)none of above

  1. (Bonus Question) Matthew argued that the interval from problem 16 is too wide. Is there anything we can do to reduce the length while keep the same confidence level?

(a) take a t confidence interval instead.

(b)use a different sample.

(c)decrease the sample size

(d) Increase the sample size

19-20. Do SAT coaching classes work? Do they help students to improve their test scores? Four students were selected randomly from all of the students that completed an SAT coaching class. For each student, we recorded their first SAT score (before the class) and their second SAT score (after the coaching class).

Student

1 2 3 4

First SAT score 920830 1010 800

Second SAT score960910 1000 980

  1. to analyze this data, we should use

(a)the one-sample t test.

(b)t test for paired data.

(c)the two-sample t test.

(d) Any of the above are valid. It just needs to be a t since σ is unknown.

  1. The degree of freedom you are going to use for the test is

(a) 4(b) 5(c) 3(d) 7

21-22.Do SAT coaching classes work? Do they help students to improve their test scores? In a study, for eight students taking the SAT exam a second time, the improvements in test scores over the first exam were recorded. Four of these students took an SAT coaching class. The other four students did not. The records are as follows.

Improvement

1 2 3 4

Coaching class 90 100 −30 40

No coaching class 10 80 70 −20

  1. To analyze this data, we should use

(a)the one-sample t test.

(b)the matched pairs t test.

(c)the two-sample t test.

(d) Any of the above are valid. It just needs to be a t since σ is unknown.

  1. The hypotheses will be set as (1 for coaching, 2 for no coaching)

(a): vs. :

(b): vs. :

(c): vs. :

(d): vs. :

23-25.In the past decades there have been intensive antismoking campaigns sponsored by both federal and private agencies. In one study of national smoking trends, two random samples of U.S. adults were selected in different years: The first sample, taken in 1995, involved 1500 adults, of which 576 were smokers. The second sample, taken in 2000, involved 2000 adults, of which 652 were smokers. The samples are to be compared to determine whether the proportion of U.S. adults that smoke declined during the 5-year period between the samples.

Let p1 be the proportion of all U.S. adults that smoked in 1995. Let p2 denote the proportion of all U.S. adults that smoked in 2000.

  1. The hypotheses to test in this problem are

(a): vs. :

(b): vs. :

(c): vs. :

(d): vs. :

  1. Calculate the z statistic for the test?

(a)z=1.27

(b)z=2.48

(c)z=3.15

(d)z=3.56

  1. The P-value of the test for equality of the proportion of smokers in 1995 and 2000

(a).108

(b).234

(c)less than .01

(d)greater than .05

26. In preparing a report on the economy, we need to estimate the percentage of businesses that expect to hire additional employees in the next 60 days. How many randomly selected businesses do we need to contact to create a 99% confidence interval with a margin of error of 4%? If no preliminary study is made to estimate p, how large a sample should we use?

(a) 480(b) 846(c) 1037(d) 335