Salt Lake Community College MATH 1040 Final Exam Fall Semester 2011 Form E

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1 Salt Lake Community College MATH 1040 Final Exam Fall Semester 011 Form E Name Instructor Time Limit: 10 minutes Any hand-held calculator may be used. Computers, cell phones, or other communication devices are not allowed. This exam has two parts. Part I - Ten multiple choice questions Part II - Ten open ended questions Part I Instructions: Answer all ten questions. Circle the letter of the most correct answer. No partial credit will be awarded on this part of the examination. 1) A doctor at a local hospital is interested in estimating the birth weight of infants. How large a sample must she select if she desires to be 90% confident that the true mean is within ounces of the sample mean? The standard deviation of the birth weights is known to be 9 ounces. A) 55 B) 54 C) 53 D) 5 ) In a recent survey, 66% of the community favored building a health center in their neighborhood. If 14 citizens are chosen, find the probability that exactly 6 of them favor the building of the health center. A) B) 0.49 C) D)

2 3) Before opening a new dealership, an auto manufacturer wants to gather information about car ownership and driving habits of the local residents. The marketing manager of the company randomly selects 1000 households from all households in the area and mails a questionnaire to them. Of the 1000 surveys mailed, she receives 150 back. Determine the type of sampling bias. A) Undercoverage B) Response C) Nonresponse D) Sampling 4) Determine the sampling technique which is used. At a local technical school, five auto repair classes are randomly selected and all of the students from each class are interviewed. What sampling technique is used? A) Simple random B) Convenience C) Cluster D) Stratified E) Systematic 5) The table lists the smoking habits of a group of college students. Sex Non-Smoker Regular Heavy Total Smoker Smoker Man Woman Total If a student is chosen at random, find the probability of getting someone who is a man or a heavy smoker. Round your answer to three decimal places. A) 0.63 B) C) D) ) Which is not a measure of dispersion? A) Mean B) Range C) Variance D) Standard deviation

3 7) Suppose that prices of a certain model of new homes are normally distributed with a mean of $150,000. Find the approximate percentage of buyers who paid between $148,700 and $151,300 if the standard deviation is $1300. A) 34% B) 68% C) 95% D) 99.7% 8) The following graph shows the number of car accidents occurring in one city in each of the years 001 through 006. How is the bar graph misleading? A) The horizontal axis is manipulated such that differences in bar heights appear larger than they really are. B) The horizontal axis is manipulated such that differences in bar heights appear smaller than they really are. C) The vertical axis is manipulated such that differences in bar heights appear larger than they really are. D) The vertical axis is manipulated such that differences in bar heights appear smaller than they really are. 9) Investing is a game of chance. Suppose there is a 30% chance that a risky stock investment will end up in a total loss of your investment. Because the rewards are so high, you decide to invest in four independent risky stocks. Find the probability that at least one of your four investments becomes a total loss. A) B) C) D)

4 10) Determine whether the situation depicts an observational study or an experiment. A medical researcher obtains a sample of adults suffering from diabetes. She randomly assigns 5 people to a treatment group and 5 to a placebo group. The treatment group receives a medication over a period of three months and the placebo group receives a placebo over the same time frame. At the end of three months the patients' symptoms are evaluated. A) observational study B) experiment End Part I Part II Instructions: Answer all ten questions carefully and completely. Show your work. Clearly indicate your answer. Partial credit may be awarded. Unless otherwise instructed, round answers to two decimal places. 11) Construct the specified histogram. The 30 students in Mrs. Harrison's literature class were asked how many cousins they had. The results are shown below. Create a frequency histogram for the data using 0 as the first lower class limit and a class width of. Include appropriate labels Describe the shape of the distribution. 4

5 1) The test scores of 30 students are listed below Compute the five-number summary. Draw a boxplot that represents the data Describe the shape of the distribution. 13) In a random sample, 10 employees at a local plant were asked to compute the distance they travel to work to the nearest tenth of a mile. The data is listed below Mean Range Sample Standard Deviation 14) A student scores 74 on a geography test and 67 on a mathematics test. The geography test has a mean of 80 and a standard deviation of 5. The mathematics test has a mean of 300 and a standard deviation of. If the data for both tests are normally distributed, on which test did the student score better relative to the other students in each class? Show your work. 5

6 15) The data below are the average one-way commute times (in minutes) for selected students and the number of absences for those students during the term. Commute time (min), x Number of absences, y Write the equation of the regression line for the given data. What would be the predicted number of absences if the commute time was 95 minutes? Round the predicted number of absences to the nearest whole number. Show your work. Linear Correlation Coefficient (3 decimal places) Critical Value Is there a significant linear relation between commute time and number of absences? Explain: 16) Claim: The mean cost of textbooks for one class is less than $180. H 0 : µ = $180 H 1 : µ < $180 In terms of this situation, explain a type I error. In terms of this situation, explain a type II error. 6

7 17) Construct a 95% confidence interval for the population mean, µ. Assume the population has a normal distribution. A sample of 40 randomly selected English majors has a mean test score of 81.5 with a standard deviation of 10.. Calculate the margin of error. Show your work. State the interval. Show your work. Interpret your result. 7

8 18) An article in a Florida newspaper reported on the topics that teenagers most want to discuss with their parents. The results of a poll showed that 46% would like more discussion about the family's financial situation, 34% would like to talk about school, and 30% would like to talk about religion. These and other percentages were based on a national random sampling of 507 teenagers. Estimate the proportion of all teenagers who want more family discussions about school using a confidence interval. Use a 95% confidence level. Calculate the margin of error. Show your work. State the interval. Show your work. Interpret your result. 8

9 19) A manufacturer claims that the mean lifetime of its lithium batteries is 1400 hours. A homeowner thinks it may be different from 1400 hours. He randomly selects 40 of these batteries and finds the mean lifetime to be 1370 hours with a standard deviation of 80 hours. Test the manufacturer's claim. Use α = Method used: Classical or P-Value (Circle one) Null Hypothesis: Alternative Hypothesis: Test Statistic: Critical Value(s) or P-Value (Circle one) Conclusion about the Null Hypothesis: Conclusion Addressing the Original Claim: 9

10 0) The engineering school at a major university claims that at least 0% of its graduates are women. In a randomly selected graduating class, of the 15 students, 50 were females. Does this suggest that the school's claim is believable? Use α = Give a detailed argument. Show all the steps. 10

11 Copyright 010 Pearson Education, Inc. Tables and Formulas for Sullivan, Statistics: Informed Decisions Using Data 010 Pearson Education, Inc Chapter Organizing and Summarizing Data Relative frequency = frequency sum of all frequencies Class midpoint: The sum of consecutive lower class limits divided by. Chapter 3 Numerically Summarizing Data Population Mean: m = gx i N Weighted Mean: x w = gw ix i gw i Sample Mean: Range = Largest Data Value - Smallest Data Value Population Variance: Sample Variance: x = gx i n s = g1x i -x n - 1 Population Standard Deviation: Sample Standard Deviation: s = g1x i -m N s = s s = s Empirical Rule: If the shape of the distribution is bellshaped, then Approximately 68% of the data lie within 1 standard deviation of the mean Approximately 95% of the data lie within standard deviations of the mean Approximately 99.7% of the data lie within 3 standard deviations of the mean Population Mean from Grouped Data: m = gx if i gf i Sample Mean from Grouped Data: x = gx if i gf i = = gx i - 1 gx i N N gx i - 1gx i n n - 1 Population Variance from Grouped Data: s = g1x i -m f i gf i = Sample Variance from Grouped Data: s = g1x i -m f i Agf i B - 1 Population z-score: Sample z-score: Interquartile Range: = z = x -x s Lower fence =Q Lower and Upper Fences: IQR Upper fence =Q IQR Five-Number Summary gx if i - 1gx if i gx if i - 1gx if i gf i gf i - 1 z = x -m s gf i gf i IQR =Q 3 -Q 1 Minimum, Q 1, M, Q 3, Maximum CHAPTER 4 Describing the Relation between Two Variables Correlation Coefficient: r = a ax i -x s x ba y i -y s y b n - 1 Residual = observed y - predicted y =y-yn R =r for the least-squares regression model yn =b 1 x +b 0 The equation of the least-squares regression line is yn =b 1 x +b 0, where yn is the predicted value, is the slope, and b 0 =y-b 1 x is the intercept. b 1 =r# s y s x The coefficient of determination, R, measures the proportion of total variation in the response variable that is explained by the least-squares regression line. CHAPTER 5 Probability Empirical Probability Classical Probability frequency of E P1E L number of trials of experiment number of ways that E can occur P1E = number of possible outcomes = N1E N1S Addition Rule for Disjoint Events P1E or F =P1E +P1F Addition Rule for n Disjoint Events P1E or F or G or Á =P1E +P1F +P1G + Á General Addition Rule P1E or F =P1E +P1F -P1E and F

12 Copyright 010 Pearson Education, Inc. Tables and Formulas for Sullivan, Statistics: Informed Decisions Using Data 010 Pearson Education, Inc Complement Rule P1E c = 1 -P1E Multiplication Rule for Independent Events P1E and F =P1E# P1F Multiplication Rule for n Independent Events P1E and F and G Á =P1E# P1F # P1G # Á Conditional Probability Rule P1E and F N1E and F P1FƒE = = P1E N1E General Multiplication Rule P1E and F =P1E# P1FƒE Factorial n! =n# 1n - 1 # 1n - # Á # 3 # # 1 Permutation of n objects taken r at a time: Combination of n objects taken r at a time: n! nc r = r!1n -r! Permutations with Repetition: n! n 1!# n!# Á# nk! np r = n! 1n -r! CHAPTER 6 Discrete Probability Distributions Mean (Expected Value) of a Discrete Random Variable m X = gx# P1x Variance of a Discrete Random Variable s X = g1x -m # P1x = gx P1x -m X Binomial Probability Distribution Function CHAPTER 7 P1x = n C x p x 11 -p n-x The Normal Distribution Standardizing a Normal Random Variable z = x -m s CHAPTER 8 Sampling Distributions Mean and Standard Deviation of the Sampling Distribution of x m x =m and s x = s n Sample Proportion:pN = x n Mean and Standard Deviation of a Binomial Random Variable m X =np s X =4np11 -p Poisson Probability Distribution Function P1x = 1ltx e -lt x = 0, 1,, Á x! Mean and Standard Deviation of a Poisson Random Variable m X =lt s X = lt Finding the Score: x =m+zs Mean and Standard Deviation of the Sampling Distribution of pn m pn =p and s pn = C p11 -p n CHAPTER 9 Estimating the Value of a Parameter Using Confidence Intervals Confidence Intervals Sample Size A 11 -a# 100% confidence interval about m with s To estimate the population mean with a margin of error E known is x ;z a/ # s. 1n at a level of confidence: n = a z # a/ s 11 -a# 100% E A 11 -a# b 100% confidence interval about m with s rounded up to the next integer. unknown is x ;t a/ # s. Note: t a/ is computed using 1n To estimate the population proportion with a margin n - 1 degrees of freedom. of error E at a 11 -a# 100% level of confidence: A 11 -a# 100% confidence interval about p is pn11 -pn pn ;z a/ #. C n A 11 -a# 100% confidence interval about is 1n - 1s 1n - 6s 1s 6. x a/ x 1-a/ s n =pn11 -pna z a/ rounded up to the next integer, E b where pn is a prior estimate of the population proportion, or n = 0.5 a z a/ rounded up to the next integer when E b no prior estimate of p is available.

13 Copyright 010 Pearson Education, Inc. Tables and Formulas for Sullivan, Statistics: Informed Decisions Using Data 010 Pearson Education, Inc CHAPTER 10 Testing Claims Regarding a Parameter Test Statistics z 0 = x -m 0 s single mean, s known n1n t 0 = x -m 0 s single mean, s unknown n1n z 0 = pn -p 0 p p 0 C n 1n - x 1s 0 = s 0 CHAPTER 11 Inferences on Two Samples Test Statistic for Matched-Pairs data where d is the mean and s d is the standard deviation of the differenced data. Confidence Interval for Matched-Pairs data: Note: is found using n - 1 degrees of freedom. t a/ t 0 = d -m d s dn1n d ;t a/ # s d 1n Test Statistic Comparing Two Means (Independent Sampling): t 0 = 1x 1 -x -1m 1 -m + s Cn 1 Confidence Interval for the Difference of Two Means (Independent Samples): s 1 s 1 1x 1 -x ;t a/ + s Cn 1 n n Note: t a/ is found using the smaller of n 1-1 or n - 1 degrees of freedom. Test Statistic Comparing Two Population Proportions z 0 = pn 1 -pn - (p 1 -p ) 4pN11 -pn B 1 n n where Confidence Interval for the Difference of Two Proportions 1pN 1 -pn ;z a/ C Test Statistic for Comparing Two Population Standard Deviations F 0 = s 1 Finding a Critical F for the Left Tail pn pn 1 n 1 + pn 11 -pn n F 1-a,n1-1,n - 1 = s 1 F a,n - 1,n 1-1 pn = x 1 +x n 1 +n. CHAPTER 1 Inference on Categorical Data Expected Counts (when testing for goodness of fit) E i =m i =np i for i = 1,, Á, k Expected Frequencies (when testing for independence or homogeneity of proportions) 1row total1column total Expected frequency = table total Chi-Square Test Statistic x 0 = a 1observed - expected expected i = 1,, Á, k = a 1O i -E i All E i Ú 1 and no more than 0% less than 5. E i CHAPTER 13 Comparing Three or More Means Test Statistic for One-Way ANOVA Mean square due to treatment F = Mean square due to error where = MST MSE Test Statistic for Tukey s Test after One-Way ANOVA q = 1x -x 1-1m -m 1 s #a = b A n 1 n x -x 1 s #a b A n 1 n MST = n 11x 1 -x +n 1x -x + Á +n k 1x k -x k - 1 MSE = 1n 1-1s 1 +1n - 1s + Á +1n k - 1s k n -k

14 Copyright 010 Pearson Education, Inc. Tables and Formulas for Sullivan, Statistics: Informed Decisions Using Data 010 Pearson Education, Inc Table I Random Numbers Column Number Row Number Table II Critical Values for Correlation Coefficient n n n n

15 Copyright 010 Pearson Education, Inc. Tables and Formulas for Sullivan, Statistics: Informed Decisions Using Data 010 Pearson Education, Inc Area z Table V Standard Normal Distribution z Confidence Interval Critical Values, z A/ Level of Confidence Critical Value, z A/ 0.90 or 90% or 95% or 98% or 99%.575 Hypothesis Testing Critical Values Level of Significance, A Left Tailed Right Tailed Two-Tailed

16 Copyright 010 Pearson Education, Inc. Tables and Formulas for Sullivan, Statistics: Informed Decisions Using Data 010 Pearson Education, Inc Area in right tail t Table VI t-distribution Area in Right Tail df z

17 Form E 1. A. D 3. C 4. C 5. B 6. A 7. B 8. C 9. A 10. B 11. Skewed Right Skewed Left 13. Mean=3.58 Range = 5. s= Z g =-1. Z m =-1.1 Better on math 15. Y=4.5x-30.3 when x=95 y 1 r=.980 critical value=.666 Yes, because.980> A Type I error would be to conclude the mean is less than $180 when in fact it is equal to $180. A Type II error would be to conclude the mean is equal to $180 when in fact it is less than $ E=3.6 (78.4, 84.76) We are 95% confident that the * 18. E=0.04 (0.30, 0.38) We are 95% confident that the * 19. H o : μ=1400 H 1 : μ 1400 t o =-.37 Critical values -.03 &.03 or p-value=0.0 Reject H o. There is sufficient evidence to conclude that the mean is not equal to 1400 hours.* 0. H o : p=0. H 1 : p>0. Critical Value= Test Statistic z o =.5 Reject H o. There is sufficient evidence to conclude that more than 0% of the graduates are female.* *Check for the phrasing you have taught.