Midterm+Exam+1+Review+%28Answer+Key%29

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Statistics

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Apr 3, 2024

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Midterm Exam 1 Review Questions (Answer Key) Chapter 1 1. Consumer Reports announced the average gas mileage of the top selling mini-vans for each U.S. car manufacturer. They used data from a sample of 50 vehicles to create their report. a) What are the observational units in this study? Each mini-van is an observational unit. b) Is the variable “average gas mileage” a categorical or quantitative variable? quantitative c) Is the variable “average gas mileage” a discrete or continuous variable? continuous 2. For each of the following statements determine if the underlined numerical values represents a parameter or a statistic. a) A study of 6076 adults in public restrooms (in Atlanta, Chicago, New York City and San Francisco) found that 23% did not wash their hands before exiting. statistic b) In a poll of all 2000 students at a high school it was found that 94% owned a cell phone. parameter c) Ty Cobb is one of Major League Baseball’s greatest hitters of all time with a career batting average of 0.366. parameter d) In a survey of 1011 people age 50 or older, 73% agreed with the statement “I believe in life after death.” statistic 3. In a Gallup News Service survey, 1017 randomly selected American adults aged 18 years or over were asked, “Of every tax dollar that goes to the federal government, how many cents of each dollar would they say are wasted?” Of the 1017 individuals surveyed, 35% indicated that 51 cents or more is wasted. Gallup poll reported that 35% of all adult Americans 18 years or older believe the federal government wastes at least 51 cents of each dollar spent. a) What is the population? All American adults aged 18 years or over b) What is the sample? 1017 selected American adults aged 18 years or over c) Which sampling method is used? (CIRCLE ONE) Cluster Multi-Stage Simple Random Stratified Systematic d) Is this an Observational Study or Experiment? (CIRCLE ONE) 4. A manager at Fresh Market wants to conduct a study regarding the shopping habits of her customers. She selects the first 60 customers who enter her store on a Saturday morning. a) What type of bias exists here? Sampling bias due to convenience sampling b) How could bias be affecting the results of the study? Saturday morning shoppers may have different shopping habits than those who come in at other times of the day or week. c) How could you improve the sampling method? Example: Randomly choose 5 shoppers each hour of each day throughout the week. Chapter 2 5. A statistics professor runs a hypothesis test to see if the proportion of times a player chooses “scissors” in the game Rock, Paper, Scissors is less than 1/3. The hypotheses tested are H 0 : p = 1/3 versus H A : p < 1/3. Would the following conclusions be a Type I Error, a Type II Error, or a correct decision? a) Conclude that the proportion is less than 1/3 when it actually equals 1/3. (Circle one) TYPE I ERROR TYPE II ERROR CORRECT DECISION b) Conclude that the proportion is less than 1/3 when it actually is less than 1/3. (Circle one) TYPE I ERROR TYPE II ERROR CORRECT DECISION c) Do not conclude that the proportion is less than 1/3 when it actually equals 1/3. (Circle one) TYPE I ERROR TYPE II ERROR CORRECT DECISION d) Do not conclude that the proportion is less than 1/3 when it actually is less than 1/3. (Circle one) TYPE I ERROR TYPE II ERROR CORRECT DECISION

6. The SLCC Math Department wants to find out which format of classes students prefer. They select a random sample of 124 current SLCC math students and ask them in which format they would prefer to take their math classes. a) Complete the relative frequency distribution. b) A bar plot with relative frequency is provided. c) How many students prefer Broadcast or Online formats? 56 d) What percentage of students prefer On-campus instruction? 25.81% 7. In a study of the habits of adults 19 years of age or older, it was determined that 241 of 1000 adults confessed to bringing their cell phone to the bathroom on every trip. What is the point estimate for the proportion of adults 19 years of age or older who bring their cell phone to the bathroom each time? 0.241 8. The p-value of a test of significance is: a) The probability, assuming the null hypothesis is true, that we observe data at least as favorable to the alternative hypothesis as the data actually observed. b) The probability, assuming the alternative hypothesis is true, that we observe data at least as favorable to the null hypothesis as the data actually observed. c) The probability the null hypothesis is true. d) The probability the null hypothesis is false. 9. Suppose you are testing to see if your dog, Hope, understands a human pointing towards an object. You use two objects and point towards one of them. If Hope goes to the one you are pointing at, you consider it a success. You put Hope through 20 trials and 13 times (or 65%) she goes to the correct object. a) Write the hypotheses using symbols to test whether Hope does better than just guessing. ࠵? ! : ࠵? = 0.5 ࠵? " : ࠵? > 0.5 b) You generate the simulation at the right using an applet. (Note this null distribution uses only 100 simulated samples and not the usual 1000 or 10,000.) Circle the dots on this null distribution that represent the numerator of your p-value. c) What is the p-value for your test? 0.12 d) Based on this p-value, should you reject or fail to reject the null hypothesis using ࠵? = 0.05 ? e) What conclusion can you make? Fail to reject ࠵? ! . There is not sufficient evidence to conclude that the proportion of times Hope understands a human pointing to an object is greater than 0.5. Class Format Frequency Relative Frequency On-campus 56 0.4516 Broadcast 24 0.1935 Hybrid 12 0.0968 Online 32 0.2581

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