Deck 7: Variation in Repeated Samplessampling Distributions

Question 1

A numerical feature of a population is called a ______.

Answer 1

statistic

Question 2

Identify the following as either a parameter or a statistic.
Sample interquartile range

Answer 2

Statistic

Question 3

In a recent year, 70% of the world's largest companies were foreign

A) The 10 companies are the population.
B) The 10 companies are a sample.

Answer 3

The 10 companies are the population.

Question 4

From the set of numbers {5, 9, 15}, a random sample of size two will be selected with replacement. Determine the sampling distribution of X̄, that is, complete the following table. (Write the probabilities as fractions.)

Question 5

A random sample of size two was selected, with replacement, from the set of numbers {2, 6, 18}. All possible samples are shown below.

A) Evaluate X̄ for each.

B) Evaluate S² for each

Question 6

A random sample of size two was selected, with replacement, from the set of numbers {12, 16, 24}. All possible samples are shown below together with $\bar{x}$ and s².

A) Determine the sampling distribution of $\bar{x}$ .

B) Determine the sampling distribution of S².

Question 7

The number of students per classroom in a mid-size college is a random variable whose distribution is normal with mean 34 students and standard deviation 4 students. You intend to visit twenty five classrooms, what is the probability that the average number of students per room will be greater than 35.3 students?

A) 0.9484
B) 0.0516
C) 0.9485
D) 0.0515

Question 8

The normal approximation is usually adequate when the sample size n is greater than 30.

Question 9

A large retail store recorded the daily average amount of money spent by its customers in December. The data suggest that the amount of money spent daily can be modeled as a distribution with mean $46 and standard deviation $5.5.
If a random sample of size 75 is selected, what is the probability that the sample mean will lie between 44 and 48? Round your answer to four decimal places.

Question 10

Extensive data suggest that the number of overtime hours paid by a large company per month can be modeled as a distribution with mean 4.2 and standard deviation 1.1.
If P₁ is the probability that the mean of a sample of size 55 lies in the interval (3.6, 4.8) and P₂ is the probability that the mean of a sample of size 110 lies in the interval (3.6, 4.8), then

A) P₁ = P₂
B) P₁ > P₂
C) P₁ < P₂
D) P₁ = 2P₂

Question 11

Data associated with gold daily price per gram during the last five years indicates a distribution with mean $32.52 and standard deviation $7.42. What is the standard deviation of $\bar{x}$ when it is based on a random sample of size n = 196?

A) 0.04
B) 2.32
C) 0.01
D) 0.53

Question 12

Data about the price of a round-trip ticket Atlanta-Barcelona, suggests that a plausible model, for X = price, is a population distribution having mean μ= $689.61 and standard deviation σ =$34.29.

A) Calculate the expected value of $\bar{x}$ for a random sample of size 66.
B) Calculate the standard deviation of $\bar{x}$ for a random sample of size 66.

Question 13

The data suggests than one plausible model, for X, the number of named storms during hurricane season in a year, is a population distribution having mean $\mu$ and standard deviation $\sigma$ . If the standard deviation for a random sample of size 85 is 1.5, what is the standard deviation for a random sample of size 340?

A) 0.38
B) 6.00
C) 0.75
D) 1.50

Question 14

Suppose the number of books consulted by a student last weekend has distribution
Let X₁ and X₂ be independent and each have the same distribution as the population.
Determine the missing elements in the table for the sampling distribution of .

Question 15

Suppose the number of coffee drinks ordered by a student yesterday has the distribution
Let X₁ and X₂ be independent and each have the same distribution as the population.
Find the expected value of $\bar{x}$ .

Question 16

Suppose the number of evenings that a student studied last weekend has distribution

A) The expected value of $\bar{x}$ .
B) If the sample size is increased to 48, give the standard deviation of $\bar{x}$ . Round your answer to three decimal places.

Question 17

The number of calories in a salad sold in the student cafeteria has a normal distribution with mean 145 and standard deviation 6.5. For a sample of size 4, determine the the expected value of X.

Question 18

The number of calories in a salad sold in the student cafeteria has a normal distribution with mean 145 and standard deviation 6.3. For a sample of size 9, determine the

A) standard deviation of X.
B) Specify the distribution of X.

Question 19

Suppose the number of passengers in a bus, going from New York City to Washington D.C., is approximately normal with mean 30.4 passengers and standard deviation 1.1 passengers. What proportion of the busses travel with less than 30 passengers?

Question 20

The heights of male students at a university have a nearly normal distribution with
mean 70.5 inches and standard deviation 2.8 inches. If 5 male students are randomly
selected to make up an intramural basketball team, what is the probability that the
heights of the team averages over 72.0 inches?

Question 21

Suppose the number of passengers in a bus, going from New York City to Washington D.C., has a normal distribution with mean 30.7 passengers and standard deviation 1.1 passengers. If two busses in this route are randomly selected, what is the probability that the average number of passengers is less than 30 passengers? Round your answer to four decimal places.

Question 22

A car manufacturer receives, in its facilities, S.U.V's for maintenance. The daily number of rear suspensions they fix per day has probability distribution
(a) Find the expected number of rear suspensions fixed per day.
(b) What is the approximated distribution of for a sample of size 40?

Question 23

The daily number of persons who file complaints about the food quality at one fast food location has probability distribution
Find the standard deviation of the number of complaints. Round your answer to one decimal place.

Question 24

A car manufacturer receives, in its facilities, S.U.V's for maintenance. The daily number of rear suspensions they fix per day has probability distribution
What is the probability distribution of total number of rear suspensions fixed in two days? Assume the number of rear suspensions fixed on different days are independent.

Question 25

The daily number of persons who file complaints about the food quality at one fast food
location has probability distribution
What is the approximate probability that this fast food location will receive more than 140 complaints in a period of 100 days?

Question 26

Suppose the weights of the contents of cans of mixed nuts have a normal distribution with mean 40 ounces and standard deviation
.5 ounce. For a random sample of size n = 16
(a) What are the mean and standard deviation of $\bar{x}$
(b) What is the distribution of $\bar{x}$ Is this distribution exact or approximate? Give your reasoning.
(c) Find the probability that $\bar{x}$ lies between 39.75 and 40.25.

Question 27

A random sample of size 225 is taken from the population of the ages of seniors enrolled at a large university one semester. This population has mean 22.3 years and standard deviation 2.5. The population distribution is not normal.
(a) Is it reasonable to assume a normal distribution for the sample mean $\bar{x}$ Why or why not?
(b) Find the probability that $\bar{x}$ lies between 22.1 and 22.5 years.

(c) Find the probability that $\bar{x}$ exceeds 22.7 years.

Question 28

A population has distribution
Let X₁ and X₂ be independent and each have the same distribution as the population.

(a) Find the expected value and variance of X₁.
(b) Determine the missing elements in the table for the sampling distribution of $\bar{X}$ = (X1 + X2) / 2

(c) Find the expected value and variance of $\bar{X}$ .
(d) If the sample size is increased to 25, give the mean and variance of $\bar{X}$

Question 29

A population has distribution

Let X₁ and X₂ be independent and each have the same distribution as the population.
(a) Find the expected value and variance of X₁.
(b) Determine the missing elements in the table for the sampling distribution of $\bar{X}$ = (X1 + X2) / 2
(c) Find the expected value and variance of $\bar{X}$ .
(d) If the sample size is increased to 16, give the mean and variance of $\bar{X}$

Question 30

Take a random sample of size n = 2, without replacement, from
{0, 2, 4, 6}. Let $\bar{x}$ = mean of the two numbers selected.
(a) List the six possible $\bar{s}$ amples and the associated value of the sample mean.
(b) Construct the sampling distribution of $\bar{x}$ .
(c) Obtain the expected value of $\bar{x}$ using the sampling distribu- tion in Part b.
(d) Obtain the variance of $\bar{x}$ using the sampling distribution in Part b.

Question 31

Take a random sample of size n = 2, without replacement, from
{1, 3, 5}. Let $\bar{X}$ = sample range.
(a) List all possible samples and the associated value of the sample range.
(b) Construct the sampling distribution of the sample range.
(c) Obtain the expected value of the sample range using the sampling distribution in Part b.