FINAL Exam Spring 2017

NAME:

MATH 250 Elements of Statistics

Multiple Choice.  Due to alternate methods of computation, there may be slight differences in answers.  Choose the letter of the best answer, and type it in the blank to the left of the problem number. Please do not add the “dot” (for example just type A instead of A. ). Also please do not change the spacing by inserting new row.  Work should be shown out to the right of the question as needed.  Hypothesis testing templates are provided on the next worksheet.

1.      Which one of the following describes a quantitative, discrete variable?

A.       Eye color

B.      Weights of new-born babies

C.       License plate numbers

D.      Number of vehicles on the Kansas Turnpike

2.      A recent poll of 700 drivers on the Kansas Turnpike was conducted by selecting every 50th vehicle.  Identify the type of sampling method used.

A.       Convenience sampling

B.       Stratified sampling

C.       Systematic sampling

D.       Random sampling

Problems 3 and 4 refer to the following data:

The following are speeds (miles per hour) of cars measured with a radar gun on the Kansas Turnpike.

70
78
76
74
79
79
74
78
77
75

3.      Find the mean and median to the nearest tenth for this sample data.

A.
Mean = 77, Median = 76.5
B.
Mean = 76, Median = 76.5

C.
Mean = 77, Median = 79.0
D.
Mean = 76, Median = 79.0

4.      Which of the following gives the sample standard deviation and the range of the data?

A.       SD = 3.2

B.  SD = 2.8
C.  SD = 3.2
D.  SD = 2.8

      Range = 11

Range = 9

Range = 9

Range = 11

5.      A researcher obtains data by examining police records for the last ten years on violent crimes during Spring Breaks. Identify the types of study for this description.

A.       Observational and Retrospective

B.    Observational and Prospective

C.    Experimental and Cross-sectional

D.    Experimental and Retrospective

   6.      The following frequency distribution summarizes credit rating scores for 20 randomly chosen subjects. Estimate the mean credit rating score by using class midpoints for credit rating scores.

Credit rating scores
Frequency

500 – 549
1

550 – 599
1

600 – 649
1

650 – 699
4

700 – 749
5

750 – 799
5

800 – 849
3

A.       Mean = 674.5
B.  Mean = 699.0
C.  Mean = 719.5
D.  Mean = 749.5

Problems 7 and 8 refer to the following histogram, which represents test scores on a recent statistics test.

7.      Identify the percent of scores that are less than or equal to 70.

A.       41.7%
B.   58.3%
C.  70.0%
D.  38.7%

8.      Within which test score group would the first quartile (Q1) fall?

A.       11-20                  B.    21-30                  C.    41-50                 D.     51-60

Problems 9 and 10 refer to the following box-and-whisker plots that compare the pulse rates of males and females.

Male pulse rate

  49       55
…….60
…………..79

101

Female pulse rate

  52
   …66
…… .75
84
98

9.      Which distribution shape best describes the boxplot Female pulse rate?

A.      Skewed right

C.      Uniform

B.      Skewed left

D.      Normal

10.      Which of the following statements is false concerning the box-and-whisker plots?

A.      Male pulse rate has a larger interquartile range (IQR) than the IQR of female pulse rate

B.      Male pulse rate has a larger median than female pulse rate

C.      Male pulse rate has a larger maximum than female pulse rate

D.      Male pulse rate has a smaller Q3 than female pulse rate

11.      Out of 40 randomly chosen patients age 65 or older, at most 20% were diagnosed to be obese. What is the complement of this description?

A.      Eight or fewer patients are obese.

B.      Fewer than eight patients are obese.

C.      More than eight patients are obese.

D.      None of the above.

, which one of the following statements is false?

A.      The probability of the complement of A is 0.03

B.      The probability of event A happening twice in a row (with replacement) is 0.0049.

C.      A is not an “unusual” event

D.      A is not a certain event.

Problems 13 and 14 refer to the following table:

A marketing survey was conducted in order to determine the probability distribution for iPhone 6 use at FHSU.  A table has been created based on the results from 7 randomly chosen students from the FHSU campus.  The random variable x represents the numbers of students who use an iPhone 6.

Number of People (x)
0
1
2
3
4
5
6
7

Probability
0.121
0.215
0.139
0.150
0.086
0.132
0.112
?

13.      Determine the probability that all 7 students use iPhone 6 so that this data set represents a legitimate probability distribution.

A.       0.065
B.      0.055
C.       0.045
D.      0.035

14.      Determine the expected number (mean) of students who use iPhone 6.

A.       3.858
B.      2.934
C.       4.812
D.      5.146

     15.      One card is randomly chosen from a standard deck of 52 cards.  If the cards are drawn without replacement, what is the probability that one King and an Ace card are chosen in either order?

A.

B.

D.

16.      Based on a poll, 60% of adults believe in the Devil. What is the probability of randomly selecting 4 people and none of them believe in the Devil?

A.       0.26
B.      0.0026
C.    2.6
D.     0.026

    17.  Assume that random guesses are made for 10 multiple choice questions on an ACT test and that there are 5 choices for each question with probability of success 0.35.  Find the probability that the number of correct answers is at most 4 (This problem meets all the requirements of a binomial situation.)

A. 0.514
B. 0.751
C. 0.942
D. 0.579

Problems 18 – 24 refer to the following distribution:

The heights of adult males are normally distributed with a mean of 75 inches and a standard deviation of 3.5 inches.

18.  What is the z-score that corresponds to a height of 72 inches?

A.       -2.5
B.      2.5
C.       -0.86
D.      0.86

19.  What symmetric interval about the mean will contain approximately 68% of the heights?

A.     71.5 to 78.5
B.      65.5 to 73.5
C.       68 to 82
D.      64.5 to 85.5

20.  What is the probability of randomly selecting 1 male whose average height is at least 6’1” tall?

A.       0.7161
B.      0.6914
C.       0.9431
D.      0.2838

21.  Which height is at the 60th percentile (rounded to the nearest whole number)?

A.       76
B.      70
C.       72
D.      68

22.  What percentage of heights are between 66 inches and 74 inches?

A.       15%
B.      38%
C.       19%
D.      12%

    23.  Suppose random samples of 16 male heights are selected repeatedly from the population. What is the mean and standard deviation for the sampling distribution of sample means?

 A.
Mean = 75, SD = 3.5

C.
Mean = 72, SD = 16

B.
Mean = 72, SD = 4

D.
Mean = 75, SD = 0.875

24.  What is the probability of randomly selecting 16 males whose average height is at most 72 inches?

A.       0.0003
B.      0.9995
C.       0.8043
D.      0.1957

Problems 25 – 27 refer to the following situation:

Suppose you want to determine the average home run percentage for the Royals baseball team. You randomly select 50 players from Royals history and determine that the mean number of home runs per 100 times at bat is 7.64.

25.  Compute a 95% confidence interval for the mean home run percentage, given that the sample standard deviation was

A.       7.64 ± 1.48
B.      7.64 ± 2.17
C.       7.64 ± 4.17
D.      7.64 ± 2.09

26.  Assume the population standard deviation is estimated to be

 How large a sample, n, should be used to obtain a margin of error of 2 with 95% confidence?

A. 31
B. 45
C. 205
D. 257

27.  Consider the situation given in Problem #26. Which of the following would produce a confidence interval with a smaller margin of error?

   A. Using a confidence level of 90%

C. Using a larger sample size

 B. Using a smaller estimate for σ

D. All of the above A-C

28.  Which of the following statements is TRUE?

A.      The Central Limit Theorem states that a sampling distribution will not have the same shape as the population distribution from which it is taken.

B.      The Central Limit Theorem states that the mean of a sampling distribution of means will have the same mean as the population distribution from which it is taken.

C.      The Central Limit Theorem states that the standard deviation of a sampling distribution of means (with

           will have a larger standard deviation than the population distribution from which it is taken.

D.      None of A-C is true.

29.  If your population is normally distributed, which of the following statements regarding confidence intervals of population means is always FALSE?

           A.   When       is known, we use the critical value

           B.   When                 we use the critical value

           C.   When               we use the critical value

           D.   None of A-C is always false.

    30.  POPT Popcorn is trying to determine the probability that the kernels of popcorn will pop. A margin of error of at most 2% is desired. How many kernels must  be sampled to meet this requirement at the 99% confidence level if no preliminary estimate of       is known?

A.       1537
B.      39
C.      4145
D.       3851

   31.  In a marketing survey, a random sample of 850 shoppers revealed that 688 remained loyal to their favorite supermarkets during the past year. Find a 90% confidence interval for the percentage of people who will remain loyal to their supermarket.

                       B.

                          C.

                      D.

    32. The US census reported that it takes workers an average of 28 minutes to drive home from work. City officials in Los Angles believe that it takes workers in their city, on average, more than 28 minutes to drive home from work. Which of the following gives the proper alternative hypothesis to test the claim that the average length of time for workers in LA to drive home from work is greater than 28 minutes?

              A.

                         B.

                            C.

                        D.

33.  According to Facebook.com, the mean number of community pages, groups, and events that users are connected to is 80.  A random sample of 64 Facebook users showed a mean of 86 connections to community pages, groups, and events.  Assume               Compute the test statistic for this test

A.       7.98
B.      -0.63
C.       -1.25
D.      1.00

34. The National Institute on Alcohol Abuse and Alcoholism reported that 45.6% of eighth-graders had used alcohol.  A random sample of 100 eighth-graders showed that 41 of them had used alcohol.    Is there evidence that the population proportion of eighth-graders has changed?  Use                  Compute the P value for this test.

A. 0.5440
B. 0.3557
C. 0.1779
D. 0.4100

35.  Suppose for a particular hypothesis test, a = 0.04 and the P value = 0.05.  Which of the following statements is TRUE?

  A. We reject the null hypothesis.

          B. We fail to reject the null hypothesis.

       C. The observed result is “unusual”.

          D. The computed test statistic, z, does fall in the shaded critical region of the tail in the normal curve.

36. The amounts of sugar (grams of sugar per gram of cereal) and calories (per gram of cereal) were recorded for a sample of 16 different cereals.  The linear correlation coefficient is                  and the regression equation is                           , where     amounts of sugar.   The mean of the 16 amounts of sugar is 0.295 grams and the mean of the 16 calorie counts is 3.76.  What is the best predicted calorie count for a cereal with a measured sugar amount of 0.40 g?

A. 3.86 calories
B.  3.76 calories
C.  4.23 calories
D.  0.295 calories

    37. A correlation coefficient of  0.057 between two quantitative variables A and B indicates that

            A. As A increases, B tends to increase.

            B. Changes in A cause changes in B.

 C. As A increases, B tends to decrease.

            D. There is a very weak association between A and B, and change in A will not affect B.

38.  Of the scatterplot graphs below, which one represents the strongest, negative linear correlation?

A.

C.

B.

D.

Problems 39 and 40 refer to the following table:

The paired values represent the systolic blood pressure in the right and left arm of a patient.

Right
102
101
94
79
79

Left
175
169
182
146
144

39.  Compute the least squares regression line for the predicted systolic blood pressure in the left arm

A.

C.

B.

D.

40.  Calculate the correlation coefficient between the two variables.

A.      0.7518

C.       0.8671

B.            -0.7518
D.      -0.8671