## Statistics/MAT 240 FINAL EXAM REVIEW

Statistics/MAT 240 FINAL EXAM REVIEW

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Question 1: Computing various statistics (mean, median, mode, range, standard deviation, variance)

Suppose we have the following data. 3970, 4500, 3700, 3150, 3720, 2970, 4000, 4150, 3500

Compute the mean, median, mode, range, standard deviation and variance of this data set.

StatCrunch: Stats Summary Stats Columns

Answers: Mean=3740, Median=3720, Mode=None, Range=1530, Standard Deviation=483.06, Variance=233350

Question 2: Discrete and Continuous Variables

Are the following variables discrete of continuous?

1. The time it takes to fly from City A to City B

2. The number of people in a restaurant that has a capacity of 200.

Answers: The first variable is continuous (time cannot be counted but measured/calculated)

The second variable is discrete (number of people in a restaurant can be counted).

Question 3: Normal Distribution

A random variable X is normally distributed with mean ????= 50 and standard deviation ????= 7. Compute the probability that X is greater than 42, i.e. P(x > 42).

StatCrunch: Stats Calculators Normal Answers: 0.8735

MAT 240 Final Exam Review

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Question 4: Central Limit Theorem

A simple random sample of size n is drawn from a large population with mean ???? and standard deviation ???? . What is the mean and standard deviation of the sampling

distribution of ???? ̅ ?

Answers: The mean of sampling distribution ???? ̅ is ???? and the standard deviation is

???? √????

Question 5: Confidence Interval for Proportion

Construct a 99% confidence interval of population proportion for the following data.

x = 120, n = 200, level of confidence = 99%

StatCrunch: Stats Proportion Stats One Sample With Summary

Answers: Lower Limit=0.5108 Upper Limit=0.6892

Question 6: Confidence Interval for the Mean

Construct a 99% confidence interval for the mean based on following data.

11.90 29.80 27.10 16.51 14.00 8.81 15.42 20.46 14.90 33.67

30.91 14.86 17.50 15.35 9.72 19.80 14.86 8.09 10.30 18.30

StatCrunch: Stats T Stats One Sample With Data

Answers: Lower Limit= 12.86 Upper Limit= 22.37

Question 7: Hypothesis Test for Proportion

Use P-Value approach to test the hypothesis given below and answer the following question.

H0: p = 0.2 H1: p > 0.2 n = 200, x = 45, ???? = 0.1 a. Is ????????0(1−????0) ≥ 10? b. Find the P-Value

MAT 240 Final Exam Review

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c. State the conclusion

StatCrunch: Stats Proportion Stats One Sample With Summary

Answers: a. Yes b. 0.1884 c. Do not reject the null hypothesis

Question 8: Hypothesis Test for the Mean

It has been stated that the mean temperature of humans is 98.6°F. Suppose researchers now claim that the mean temperature of humans is less than 98.6°F. A total of 700

observations are collected and the sample mean is 97.5°F and a sample standard deviation of 0.7°F. Use ???? = 0.01 where applicable.

a. What are the null and alternative hypotheses? b. What is the test statistic? c. What is the critical value? Use the table and StatCrunch. d. What is the P-Value?

e. What is the conclusion?

MAT 240 Final Exam Review

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StatCrunch: Stats T Stats One Sample With Summary

Answers: a. H0: Temperature = 98.6°F H1: Temperature < 98.6°F
b. -41.58 c. Table value -2.330 StatCrunch value -2.332
d. <0.0001 (Almost 0.000) e. Reject the null hypothesis
Question 9: Confidence interval for difference in two proportions
Consider a study in which there are two groups, an experimental group and a control group. The experimental group includes subjects that receive a specific treatment,
say a new vaccine. Suppose 115 out of 716 subjects experience a side effect. The control group does not receive any treatment. Suppose that 74 out of 623 subjects
experience a side effect. Construct a 99% confidence interval for the difference between two population proportions, ????1 −????2.
StatCrunch: Stats Proportion Stats Two Sample With Summary
Answers: Lower Limit= -0.007 Upper Limit= 0.0905
Question 10: Correlation
Match the linear correlation coefficient to the scatter diagram. The scales on x-axis and y-axis are the same for each scatter diagram.
a. r = 0.946 b. r = 0.787 c. r = 1
Answers: a matches with II, b matches with III, c matches with I
MAT 240 Final Exam Review
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Question 11: Correlation
Plot a scatterplot for the following data set and compute the correlation coefficient. What type of relationship exists between x and y.
x 3 6 9 10 10 11 12 y 1.5 1.7 2.3 2.8 2.8 3.1 3.3
StatCrunch: Graph Scatterplot Stats Summary Stats Correlation
Answers:
Correlation= 0.966, A strong positive correlation exists between x and y
Question 12: Regression
For the data set in previous problem, answer the questions below.
x 3 6 9 10 10 11 12 y 1.5 1.7 2.3 2.8 2.8 3.1 3.3
a. Write a general form of regression equation without the error term. b. Find estimates of ???????? and ????????. c. Interpret the estimate of ???????? d. Compute the point estimate
for ????, i.e. the standard error. e. Compute the standard error for ????????, i.e. ????????????
MAT 240 Final Exam Review
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f. Perform a test of hypothesis for significance of the overall regression model. What are the null and alternative hypothesis? Use alpha=0.10 g. What is the
conclusion of the test? h. Assuming residuals are normally distributed, what is the average value of y if the value of x is 8. i. Compute the 90% confidence interval
for the slope of least-square regression line.
StatCrunch: Stat Regression Simple Linear Answers: a. ???? = ????????????+???????? where ???????? is the slope and ???????? is the intercept b. Estimate for ???????? is 0.2120 and ???????? 0.6524
Regression equation is ???? = ????.????????????????????+????.???????????????? c. If ???????? increases by 1 unit, then the response variable (y) will increase by 0.2120 units on average
d. 0.1942 e. 0.0252 f. Null Hypothesis: ???????? = ???? Alternative Hypothesis: ???????? ≠ ????
P-Value = 0.0004 with a Test-Statistic= 70.84
g. Since P-Value < alpha, reject the null hypothesis. The model is significant.
h. Since the model is significant and appropriate, y = 0.2120(8)+0.6524 = 2.348
i. (0.1613, 0.2628)
Question 13: Multiple Regression
Consider the following data set and answer questions that follow.
X1 3 6 9 10 10 11 12 X2 26 24 22 20 21 17 18 Y 1.5 1.7 2.3 2.8 2.8 3.1 3.3
a. What is the multiple regression equation for the data set above. b. Interpret the coefficient of ????????
MAT 240 Final Exam Review
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StatCrunch: Stat Regression Multiple Linear Answers: a. ???? = ????.????????????????????????− ????.???????????????????????? +????.???????????????? b. If ???????? increases by 1 unit, then the response variable will increase by
0.1163 units on average while holding ???????? constant.
MAT 240 Final Exam Study Guide Page 1 11 1 of 3 33 3
MAT-240 Final Exam Study Guide
Question Section Problem Type Instructor Tip HW Reference Problem 1 3.1 Determine the arithmetic mean, median, and mode of a variable from raw data. Open the data
in StatCrunch. Use Stat -> Summary Stats -> Columns. From there you can find the values in question. HW #1, Problem #6 2 3.2 Determine the range, standard deviation,

and variance of a variable from raw data. Same as question 1, just looking for measure of dispersion. HW #1, Problem #8 3 6.1 Distinguish between discrete and

continuous random variables. Recall that counts are generally discrete variables, while measurements are generally continuous Variables. HW #1, Problem #11 4 6.1

Identify discrete probability distributions. Recall that the sum of individual probabilities must be 1 (or 100%). See page 323 of text for reference. HW #1, Problem

#12 5 7.1 Graph a normal curve. Remember that the highest point of a normal curve will occur where the mean is. Meaning, if the mean is 10 the high point of the

graph will be above that value on the x-axis. HW #2, Problem #3 6 7.2 Find and interpret the area under a normal curve. In this problem, you need to change the

values to standard normal values (z-scores) and use the standard normal table to find the area or the StatCrunch Normal Calculator HW #2, Problem #7 7 8.1 Describe

the distribution of the sample mean: normal population. Review page 404 of the textbook for help on this problem. HW #2, Problem #10 8 8.2 Describe the sampling

distribution of a sample proportion. Review page 416 of the textbook for help on this problem. HW #2, Problem #13 9 9.1 Construct and interpret a confidence

interval for the population proportion. This problem can be tricky but can be easily solved using StatCrunch. Use the method shown in the video here: http://snhu-

mat240- videos.davidysze.com/9.1.7sc/9.1.7sc.html HW #3, Problem #1 10 9.1 Construct and interpret a confidence interval for the population proportion. StatCrunch

will help you solve here! Use the options: Stat -> Proportion Statistics -> One Sample -> With Summary (make sure you select confidence interval) HW #3, Problem #3 11

9.2 Construct and interpret a confidence interval for a population mean. Remember that the point estimate falls between the two bounds and the margin of error is the

difference between the upper bound and the point estimate. HW #3, Problem #9

MAT 240 Final Exam Study Guide Page 2 22 2 of 3 33 3

Question Section Problem Type Instructor Tip HW Reference Problem 12 9.2 Construct and interpret a confidence interval for a population mean. StatCrunch will help

solve this problem. Open the data in StatCrunch use the option: Stat -> T Statistic -> One Sample -> With Data HW #3, Problem #13 13 10.1 State conclusions to

hypothesis tests. Review pages 477 – 479 of the textbook. HW #4, Problem #4 14 10.2 Test hypotheses about a population proportion. StatCrunch will help you solve

here! Use the options: Stat -> Proportion Statistics -> One Sample -> With Summary (Make sure you put in the values correctly! X is the number of success and n is the

number of observations) HW #4, Problem #7 15 10.3 Test hypotheses about a mean. When answering this problem remember that if the P-value is < the level of significance (alpha) we reject the null. If it is greater than, we fail to reject the null. For this problem you will be using the StatCrunch option: Stat -> T

Statistics -> One Sample -> With Summary HW #4, Problem #14 16 10.3 Test hypotheses about a mean. Same as above, use the StatCrunch option: Stat -> T Statistics ->

One Sample -> With Summary HW #4, Problem #15 17 11.1 Distinguish between independent and dependent sampling. Make sure to review section 11.1, as it gives many

examples on how to tell the difference! Remember that a sample is independent is the individuals selected in one sample to not dictate which ones are selected in the

second. HW #5, Problem #1 18 11.1 Construct and interpret confidence intervals for the difference between two population proportions. For this problem, use the

StatCrunch option: Stat -> Proportion Statistics -> Two Sample -> With Summary HW #5, Problem #4 19 11.2 Test hypotheses regarding matched-pairs data. Remember that

t0 is the test statistic and ta is the critical value. You can find both by using the StatCrunch option: Stat -> T Statistics -> Paired. Use these values to determine

if you reject or fail to reject the null hypothesis. HW #5, Problem #8 20 11.3 Test hypotheses regarding the difference of two independent means. StatCrunch again

will help solve. Open the data in StatCrunch and use the option: Stat -> T Statistic -> Two Sample -> With Data. Use the resulting output to determine if you reject or

fail to reject the null hypothesis. HW #5, Problem #12

MAT 240 Final Exam Study Guide Page 3 33 3 of 3 33 3

Question Section Problem Type Instructor Tip HW Reference Problem 21 4.1 Compute and interpret the linear correlation coefficient. To find the value of r

(correlation coefficient) use StatCrunch and select: Stat -> Summary Stats -> Correlation. HW #6, Problem #3 22 4.1 Compute and interpret the linear correlation

coefficient. Review page 194 of the textbook. HW #6, Problem #5 23 4.2 Interpret the slope and the y-intercept of the least-squares regression line. Review pages

212 – 213 of the textbook and to find the predicted value, plug the value of the predictor variable into the regression equation! HW #6, Problem #8 24 4.3 Perform

residual analysis on a regression model. Review pages 224 – 226 of the textbook. HW #6, Problem #12 25 14.1 Compute the standard error of the estimate and conduct

inference on the slope. This problem is a little tricky. Use the normal options to compute the regression line. To find the standard error of the point estimate, you

need to take the square root of the error MS value in the second table. The other standard error is found in the first table summary. HW #7, Problem #3 26 14.1

Construct a confidence interval about the slope of the least-squares regression model. Use StatCrunch options States -> Regression -> Simple Linear. All the

information you need is in that table! HW #7, Problem #5 27 14.1 Construct a confidence interval about the slope of the least-squares regression model. Review pages

683 – 685 of the textbook. HW #7, Problem #7 28 14.3 Interpret the coefficients of a multiple regression equation. Review pages 703 – 704 of the textbook. HW #7,

Problem #8