Stats Exam 1 Practice Problems

Which of the following statements is correct?

"Random sampling" refers to the sampling scheme such that all possible samples from the population have equal chance to be drawn.

Let the random variable X represent the amount of money Dan makes doing lawn care in a randomly selected week in the summer. Assume that X is Normal with mean $240 and standard deviation $60. The probability is approximately 0.6 that, in a randomly selected week, Dan will make less than

$255

An insurance company has estimated the following cost probabilities for the next year on a particular model of car: Cost $0 $500 $1000 $2000 Probability 0.60 0.05 0.13 0.22 The expected cost to the insurance company is (approximately):

$595

It is known that 90% of first-year students at University of Minnesota live on campus. In a random sample of 73 first-year students, 61 live on campus. Which of the following statement is true?

(A) The observed sample proportion of first-year who live on campus is 61/73 = 0.8356 (B) The standard deviation of sampling distribution of sample proportion is q 0.9(1−0.9) 73 = 0.03511 (C) The mean of sampling distribution of sample proportion is 0.9. *** All of the above

About 350 students in STAT 3011 answered the question, "What is the amount of money you spent on entertainment last week (in dollars)". The smallest amount is $0 and the largest amount is $1200. Which of the following graphical summaries is/are the most appropriate for summarizing the responses on this question? (i) Stem-and-leaf plot (ii) Bar graph (iii) Boxplot (iv) Histogram

(iii) and (iv)

The events A, B, C have probabilities Pr(A) = 0.5,Pr(B) = 0.2, and Pr(C) = 0.3, respectively. It is known that: • A and B are disjoint • A and C are independent • B and C are independent Find the probability Pr (C ∩ (A ∪ B)).

0.21

Let the random variable X represent the profit made on a randomly selected day by a certain store. Assume X is Normal with a mean of $360 and standard deviation $50. Given that Pr(0 < Z < 0.8) = 0.2881, the probability that Pr(X > $400) is:

0.2119

In a large lecture, the professor has each student toss a fair coin 100 times and calculate the proportion of times the tosses come up heads. Roughly 68% of students should have proportions between which two numbers?

0.45, 0.55

Let X be the SAT score and suppose that SAT scores are known to follow a normal distribution with mean 1026 and standard deviation 209. What is the probability that a randomly selected student received a score at most 820? Z follows a standard normal distribution.

1 − P(Z ≥ −0.99)

Consider rolling two fair dice at the same time. What is the conditional probability of getting a pair, given that the total is 4 or lower?

1/3

Your neighbor has 2 children. You learn that he has a son, Joe. What is the probability that Joe's sibling is a brother?

1/3

In the same content setting as the previous question, where two cards are drawn from a standard deck of playing cards one at a time without replacement. What is the probability that the first card is heart and second card is queen?

1/52

The standard deck of playing cards consists of 52 cards. It includes 13 ranks in each of the four suits (clubs, diamonds, hearts, and spades). Each suit includes an ace, a king, queen, jack and 2 through 10. Suppose two cards are drawn from a standard deck of playing cards one at a time without replacement. What is the probability that the second card is heart given the first card is queen of heart?

12/51

The incomes of trainees at a local mill are normally distributed with a mean of $1250 and a standard deviation of $175. What percentage below is the best representation of trainees that earns less than $1000 $900 a month? (Hint: Use XX-XX-XX.X Rule)

2.58%

A bag contains six identical balls with numbers 1-6 on them. We randomly draw two balls from the bag at the same time. What is the probability that the sum of the numbers on the two balls is odd?

3/5

If data is approximately normally distributed, then about of the data is expected to fall within one standard deviation of the mean.

68%

Let A and B be events with P(A) = 0.4 and P(B) = 0.3. It is known that P(A ∪ B) = 0.58. Which of the following statements about events A and B is correct?

A and B are independent

What is an observational study?

A type of study in which individuals are observed or certain outcomes are measured. No attempt is made to affect the outcome (for example, no treatment is given).

If event A and B are disjoint and nonempty, what can we infer?

Event A and B is never independent

Sampling distribution of sample proportion for a random sample size of 50 describes

How sample proportions tend to vary from random sample to random sample of size 50

Let X be a random variable with mean µ and standard deviation σ. Let x1, x2, · · · , xn be a random sample of size n, and denote the sample mean as x. Which of the following statement about the sampling distribution of x is correct?

If X is a discrete random variable, then the sampling distribution of X is NEVER approximately normal, no matter how large the sample size n is.

Which of the following numerical summaries is resistant to outliers?

Inter-quartile range (IQR)

Which of the following is NOT a continuous random variable?

Number of coins in your pocket at any time

Which of the following variables in the American Housing Survey (AHS) is a discrete quantitative variable that takes integer values?

Number of water supply stoppages that have occurred during the past 3 months

Which of the following statements is always TRUE if events A and B are disjoint?

P(A) = P(A ∪ B) − P(B)

If the value of x from a normal random variable X is known, what else is needed to calculate the z-score of x?

Population mean and population variance

Two fair dice are rolled once each. Let events U, V , and W be defined as following: • U: The product (result of multiplying) of the outcomes of the two dice is 6 • V : The sum of the outcomes of the two dice is 8 • W: The difference between the outcomes of the two dice (larger − smaller) is 3 Sort the probabilities of U, V , and W from the largest to the smallest.

Pr(W) > Pr(V ) > Pr(U)

Which of the following numerical summary is NOT represented on boxplots?

Standard deviation

The difference between an observational and experimental study is that

an experimental study can be used to establish cause and effect, but an observational study cannot.

Select all true statements about a normal distribution. i A normal distribution can be completely determined by its mean and standard deviation. ii The total area under a normal curve depends upon its mean and standard deviation. iii The mean and the median of a normal distribution are the same. iv QQ-plots can be used to assess whether the data follow a normal distribution.

i, iii, and iv

3 randomly selected students sleep hours are following: 7, 5, 6 Calculate the sample variance of those three observations.

s 2 = P(x − x¯) 2/(n − 1) = {(7 − 6)2 + (5 − 6)2 + (6 − 6)2}/2 = (1 + 0 + 1)/2 = 1

Three datasets A, B, C are given as following. All of them have the same sample size n = 6 and sample mean x = 0. Sort the standard deviations sA, sB, sC from the smallest to the largest. • Dataset A: −3 − 3, 0, 2, 2, 2 • Dataset B: −2, −2, −2, 0, 3, 3 • Dataset C: −2, −1, 0, 0, 1, 2

sC < sA = sB

A national random sample of 6 ACT scores from 2010 is listed below. Calculate the sample mean and sample median. 29, 23, 17, 26, 14, 17

x¯ = 21, M = 20

Which of the following statements about experiments and observational studies is NOT correct?

An experiment involves two or more variables, while an observational study only involve one variable.

True or false : i As the sample size increases, the standard deviation of the sampling distribution increases. ii As the sample size increase, the sampling distribution of the sample proportion looks more like the population distribution.

Both i and ii are false.

Which of the following properties are NOT true regarding the sampling distribution of sample mean?

By the central limit theorem, the distribution of X¯ is normal for any sample size n

A poll of 1150 people between the ages of 21 and 29 asked "How concerned are you about the problem of viral outbreak?" The possible responses were 'very concerned', 'somewhat concerned', 'not very concerned', and 'haven't heard about it'. The poll reported percentages (43%, 27%, 20%, 10%) in these categories. Answer the following two questions. Identify the sample and the population

The sample is the set of 1150 people that were polled while the population is the set of all people between the ages of 21 and 29.

What is an experimental study?

a study in which conditions are controlled and manipulated by the experimenter.