Deck 8: Sampling Distributions

Question 1

Determine and from the given parameters of the population and the sample size. Round the answer to the nearest thousandth where appropriate.

-? = 69, ? = 24, n = 64

A) =8.625, =3
B) =69, =3
C) =69, =24
D) =69, =0.375

Answer 1

=69, =3

Question 2

Determine and from the given parameters of the population and the sample size. Round the answer to the nearest thousandth where appropriate.

-? = 31, ? = 8, n = 15

A) =31, =8
B) =31, =0.533
C) =17.898, =2.066
D) =31, =2.066

Answer 2

=31, =2.066

Question 3

What are the values of and for the sampling distribution of the sample mean shown?

A) =20, =490
B) =490, =20
C) =490, =40
D) =490, =60

Answer 3

=490, =20

Question 4

What are the values of and for the sampling distribution of the sample mean shown?

A) =0.04, =8
B) =8, =0.12
C) =8, =0.08
D) =8, =0.04

Question 5

The standard error of the mean is given by

A) ? -
B)
C)
D) ? ± ?

Question 6

The amount of money collected by a snack bar at a large university has been recorded daily for the past five years. Records indicate that the mean daily amount collected is $6000 and the standard deviation is $400. The distribution is skewed to the right due to several high volume days (including football game days). Suppose that 100 days were randomly selected from the five years and the average amount collected from those days was recorded. Which of the following describes the sampling distribution of the sample mean?

A) normally distributed with a mean of $6000 and a standard deviation of $400
B) skewed to the right with a mean of $6000 and a standard deviation of $400
C) normally distributed with a mean of $600 and a standard deviation of $40
D) normally distributed with a mean of $6000 and a standard deviation of $40

Question 7

A farmer was interested in determining how many grasshoppers were in his field. He knows that the distribution of grasshoppers may not be normally distributed in his field due to growing conditions. As he drives his tractor down each row he counts how many grasshoppers he sees flying away. After several rows he figures the mean number of flights to be 57 with a standard deviation of 12. What is the probability of the farmer will count 60 or more flights on average in the next 40 rows down which he drives his tractor?

A) 0.4429
B) 0.5710
C) 0.9429
D) 0.0571

Question 8

A farmer was interest in determining how many grasshoppers were in his field. He knows that the distribution of grasshoppers may not be normally distributed in his field due to growing conditions. As he drives his tractor down each row he counts how many grasshoppers he sees flying away. After several rows he figures the mean number of flights to be 57 with a standard deviation of 12. What is the probability of the farmer will count 52 or fewer flights on average in the next 40 rows down which he drives his tractor?

A) 0.0410
B) 0.9959
C) 0.0041
D) 0.4959

Question 9

A farmer was interested in determining how many grasshoppers were in his field. He knows that the distribution of grasshoppers may not be normally distributed in his field due to growing conditions. As he drives his tractor down each row he counts how many grasshoppers he sees flying away. After several rows he figures the mean number of flights to be 57 with a standard deviation of 12. What is the probability of the farmer will count 52 or fewer flights or 60 or more flights on average in the next 40 rows down which he drives his tractor?

A) 0.4959
B) 0.9388
C) 0.0612
D) 0.0530

Question 10

Describe the sampling distribution of .

-N = 20,000, n = 550, p = 0.2

A) Approximately normal; = 0.2, = 0.0894
B) Exactly normal; = 0.2, = 0.017
C) Binomial; = 110, = 9.38
D) Approximately normal; = 0.2, = 0.017

Question 11

A simple random sample of size n = 1240 is obtained from a population whose size is and whose population proportion with a specified characteristic is Describe the sampling distribution of .

A) Exactly normal; = 0.39, = 0.014
B) Approximately normal; = 0.39, = 0.014
C) Approximately normal; = 0.39, = 0.1150
D) Exactly normal; = 0.39, = 0.1150

Question 12

According to a study conducted in one city, 34% of adults in the city have credit card debts of more than $2000. A simple random sample of adults is obtained from the city. Describe the sampling distribution of , the sample proportion of adults who have credit card debts of more than $2000.

A) Exactly normal; = 0.34, = 0.027
B) Approximately normal; = 0.34, = 0.0007
C) Binomial; = 102, = 8.20
D) Approximately normal; = 0.34, = 0.027