EBook Problems EDA Statistics

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EBook Problems Set - Statistics Problems

Problem 1

A recent Gallup Poll found that 23% of senior citizens exercise at least 3 times a week. The number 23% is:

  • Choose one answer.
(a) A sample
(b) An estimate of the percentage of all senior citizens who exercise in the population
(c) The percentage of all senior citizens who exercise in the population
(d) A parameter

Problem 2

A student said his SAT Math score was at the 90th percentile. This means that:

  • Choose one answer.
(a) The student got 90% of the questions wrong
(b) 90% of the class had a lower score than the student
(c) The student got 90% of the questions right
(d) 90% of the class had a higher score than the student

Problem 3

A random sample of 1000 US adults were interviewed and it was found that 2 of them had a rare disease known as diseaseA. Which of the following is true?

  • Choose one answer.
(a) The standard error of the sample proportion is 5%
(b) 1000 is not a large enough sample to be able to construct a 99.7% confidence interval
(c) There is no way we can figure out whether the sample is too large or too small to construct an interval
(d) 2% of people in the sample have diseaseA

Problem 4

The Caldwells want to buy a new car, and they have narrowed their choices to a Buick or an Oldsmobile. They first consulted an issue of Consumer Reports, which compared rates of repairs for various cars. Records of repairs done on 400 cars of each type showed somewhat fewer mechanical problems with the Buick than with the Oldsmobile. The Caldwells then talked to three friends, two Oldsmobile owners and one former Buick owner. Both Oldsmobile owners reported having a few mechanical problems, but nothing major. The Buick owner, however, exploded when asked how he liked his car: first, the fuel injection went out, which cost $250 to fix. Next, he started having trouble with the rear end and had to replace it. He finally decided to sell it after the transmission went. He says he'd never buy another Buick. The Caldwells want to buy the car that is less likely to require repairs. Given what they currently know, which car would you recommend that they buy?

  • Choose one answer.
(a) I would recommend that they buy the Buick despite their friend's bad experience. He is just one case, while the information reported in Consumer Reports is based on many cases. According to that data, the Buick is somewhat less likely to require repair.
(b) I would recommend that they buy the Oldsmobile, primarily because of all the trouble their friend had with his Buick. Since they haven't heard similar horror stories about the Oldsmobile, they should go with it.
(c) I would tell them that it does not matter which car they bought. Even though one of the models might be more likely than the other to require repairs, they could still, just by chance, get stuck with a particular car that would need a lot of repairs.

Problem 5

5. Used cars like yours are selling for a mean price $25,000 with a standard deviation of $1,000. You plan to sell your car so that you can buy a boat in Europe. The average cost of a boat in Europe is 20,000 Euros with a standard deviation of 600 Euros. What can you expect in your pocket after the sale and subsequent purchase? One US dollar is 0.9 Euros.

  • Choose one answer.
(a) -$2,500
(b) $5,000
(c) $2,500
(d) $10,000

Problem 6

In either a survey situation or a manufacturing process, what can we do to offset a large population standard deviation to still obtain accuracy of our sample mean?

  • Choose one answer.
(a) Select a smaller sample size
(b) Give up! There is nothing you can do in this case
(c) Select a larger sample size

Problem 7

The amount of money college students spend each semester on textbooks is normally distributed with a mean of $195 and a standard deviation of $20. Suppose you take a random sample of 100 college students from this population. There is a 68% chance that the sample mean amount spent on textbooks is between:

  • Choose one answer.
(a) $155 and $235.
(b) $175 and $215.
(c) $193 and $197.
(d) $191 and $199.

Problem 8

It is known that 17.875% of job applicants lie about their academic credentials. The chance that in a simple random sample of 84 applicants between 17.806% and 17.943% lie is

  • Choose one answer.
(a) 0% chance
(b) 68% chance
(c) 99.7% chance
(d) 90% chance

Problem 9

Jim works in the admission office of a major state university in the east coast. He reports that of the 37000 undergraduates who attend this unversity, 47% are male. He then sends an email to every 10th senior and asks them if they plan to go to graduate school and he finds the percentage to be 23%.

  • Choose one answer.
(a) 47% is a parameter and 23% is a statistic
(b) 47% is a statistic and 23% is a parameter
(c) 47% and 23% are both parameters
(d) 47% and 23% are both statistics

Problem 10

Which best describes a sampling distribution model of a statistic?

  • Choose one answer.
(a) It is a distribution of all the statistics calculated from all possible samples of the same size.
(b) It is the probability distribution of all values that are contained in all possible sample of the same size.
(c) It is the probability that the sampling statistic equals the parameter of interest.
(d) It is a histogram of sample statistics from all possible samples of the same size.

Problem 11

A simple random sample of 100 students in the suburb reveals that 65% of them have at least a part time job in addition to school. If the expected value of this proportion is equal to the proportion of all students who have at least a part time job for the entire suburb, then we say that the sample proportion is:

  • Choose one answer.
(a) An unbiased estimator of the population proportion
(b) Equal to the population proportion
(c) An estimate whose variance equals the variance of the population
(d) True value
(e) Less than the population proportion since only 100 students were sampled

Problem 12

Two random samples of 50 undergraduates each from two universities are taken to determine the proportion of students who approve of the food services at their respective schools. One university had an enrollment of 5,000 and the other has 35,000 undergrads. Which is the most accurate statement?

  • Choose one answer.
(a) The proportion of students who approve of the food services will be the same since the sample sizes are the same.
(b) The enrollment figures from the two universities are not relevant to whether the sample statistics obtained are unbiased estimates of the parameters of the two populations.
(c) If a university that enrolled 100,000 undergrads conducted a random sample, the results would be less accurate than either of the samples discussed in this problem.
(d) The variability of the sample from the larger university will be greater than the variability of the sample from the smaller school.

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