Introduction to Statistics Test Questions and Answers

Introduction to Statistics Test Questions and Answers 90. When you sample so that every combination of individuals in your population has an equal chance of being chosen you are taking a: SRS 91. A friend of yours in your intro stats class obtains permission to randomly sample the University student body to conduct a satisfaction survey on some recent changes to the enrollment process. She randomly samples 50 freshmen, 50 sophomores, 50 juniors, and 50 seniors. This is an example of a: stratified sample 92. Some friends of yours in a political science class are angry about a new town ordinance restricting off-campus parties. They make an online survey asking students' opinions. This type of sampling might be classified as a: convenience sample 93. Flipping a fair coin is said to randomly generate heads and tails with equal probability. Explain what random means in this context.: In the long run, a fair coin will generate 50% heads and 50% tails, approximately. But for each flip, the outcome cannot be predicted. 94. A friend says "I flipped five heads in a row! The next one has to be tails!" Explain why this thinking is incorrect.: A friend says "I flipped five heads in a row! The next one has to be tails!" Explain why this thinking is incorrect. 95. A national survey found that 50 % of adults ages 25-29 had only a cell phone and no landline. Suppose that five 25-29-year-olds are randomly selected. Complete parts a through c below.: a) What is the probability that all of these adults have only a cell phone and no landline? (0.5)^5 = 0.0313 b) What is the probability that none of these adults have only a cell phone and no landline? 50% have only a cell phone and no landline. So 50% have none of this. (0.5)^5 = 0.0313 c) What is the probability that at least one of these adults has only a cell phone and no landline? 1-(0.5)^5 = 0.9687 96. Suppose that 19 % of people have a dog , 29 % of people have a cat , and 7 % of people own both. What is the probability that someone owns a dog or a cat ?: 0.19+0.29-0.07 = 0.41 97. What is the probability that a person likes to watch football, given that she also likes to watch basketball? Basketball 27 8 No_Basketball 39 26: 27/35 = 0.771 98. A student figures that he has a 32 % chance of being let out of class late. If he leaves class late, there is a 60 % chance that he will miss his train. What is the probability that he gets out of class late and misses the train?: 0.32 x 0.60 = 0.192 99. A nervous kicker usually makes 82 % of his first field goal attempts. If he makes his first attempt, his success rate rises to 89 %. What is the probability that he makes his first two kicks?: 0.82 x 0.89 = 0.73 100. On a certain ship that sank, the probability of survival was 0.394. Among first class passengers, it was 0.794. Were survival and ticket class independent? Explain.: No , because the probability of survival and the probability of survival given a first class passenger are not the same. 101. If the sex of a child is independent of all other births, is the probability of a woman giving birth to a girl after having four boys greater than it was on her first birth? Explain.: No, the probability after having four boys is equal to the probability on her first birth. If sex is independent of previous births, then the probability of a girl given she has had four boys must equal the probability of a girl. 102. For each of the following, list the sample space and tell whether you think the events are equally likely: a) Roll two dice; record the sum of the numbers b) A family has 3 children; record each child's sex in order of birth c) Toss four coins; record the number of tails d) Toss a coin 10 times; record the length of the longest run of heads: a) S= {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} the events are not equally likely. b) S= {BBB, BBG, BGB, BGG, GBB, GBG, GGB, GGG} the events are equally likely c) S= {0, 1, 2, 3, 4} the events are not equally likely d) S= {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} the events are not equally likely 103. A casino claims that its roulette wheel is truly random. What should that claim mean?: Every number is equally likely to occur. 104. The weather reporter on TV makes predictions such as a 25% chance of rain. What is the meaning of such a phrase?: On days with conditions such as these, rain occurs 25% of the time. 105. After an unusually dry autumn, a radio announcer is heard to say, "Watch out! We'll pay for these sunny days later on this winter." Explain what he's trying to say, and comment on the validity of his reasoning.: The radio announcer is trying to use the "Law of Averages." His reasoning is invalid; if rain in the fall and winter are independent of each other, a nice fall will have no bearing on winter rains. 106. Recently, a casino issued a press release announcing that a cocktail waitress won the world's largest slot jackpot—over $30,000,000. She said she had played less than $50 in the machine when the jackpot hit. The top jackpot for this type of slot machine builds from a base amount of $7 million and can be won with a 3-coin ($3) bet.: a) How can the casino afford to give away millions of dollars? The casino earns more than the value of the jackpot from people who bet but do not win. b) Why did the casino issue a press release rather than keep the loss a secret? The press release generates publicity, which entices more people to come and gamble. The amount the casino earns from this more than makes up for the jackpot. 107. Suppose that 36 % of families living in a certain country own a desktop computer and 21 % own a laptop. The Addition Rule might suggest, then, that 57 % of families own either a desktop computer or a laptop. What's wrong with that reasoning?: A family may own both a desktop computer and a laptop. The events are not disjoint, so the Addition Rule does not apply. 108. Funding for many schools comes from taxes based on assessed values of local properties. People's homes are assessed higher if they have extra features such as garages and hot tubs. Assessment records in a certain school district indicate that 30 % of the homes have garages and 5 % have hot tubs. The Addition Rule might suggest, then, that 35 % of residences have a garage or a hot tub. What is wrong with that reasoning?: A home may have a garage and a hot tub. The events are not disjoint, so the Addition Rule does not apply.