Question 1

A population consists of 500 elements. We want to draw a simple random sample of 50 elements from this population. On the first selection, the probability of an element being selected is

Accepted Answer

A)  0.100 
B)  0.010 
C)  0.001 
D)  0.002

Question 2

A simple random sample from an infinite population is a sample selected such that

Accepted Answer

A)  each element is selected independently and from the same population 
B)  each element has a 0.5 probability of being selected 
C)  each element has a probability of at least 0.5 of being selected 
D)  the probability of being selected changes

Question 3

A population of size 1,000 has a proportion of 0.5. Therefore, the proportion and the standard deviation of the sample proportion for samples of size 100 are

Accepted Answer

A)  500 and 0.047 
B)  500 and 0.050 
C)  0.5 and 0.047 
D)  0.5 and 0.050

Question 4

The SAT scores have an average of 1200 with a standard deviation of 60. A sample of 36 scores is selected.
a. What is the probability that the sample mean will be larger than 1224?
b. What is the probability that the sample mean will be less than 1230?
c. What is the probability that the sample mean will be between 1200 and 1214?
d. What is the probability that the sample mean will be greater than 1200?
e. What is the probability that the sample mean will be larger than 73.46?

Accepted Answer

The answer of The SAT scores have an average of...

Question 5

A probability distribution for all possible values of a sample statistic is known as

Accepted Answer

A)  a sample statistic 
B)  a parameter 
C)  simple random sampling 
D)  a sampling distribution

Question 6

A new soft drink is being market tested. It is estimated that 60% of consumers will like the new drink. A sample of 96 taste tested the new drink.
a. Determine the standard error of the proportion
b. What is the probability that more than 70.4% of consumers will indicate they like the drink?
c. What is the probability that more than 30% of consumers will indicate they do not like the drink?

Accepted Answer

The answer of A new soft drink is being market...

Question 7

A simple random sample of 64 observations was taken from a large population. The sample mean and the standard deviation were determined to be 320 and 120 respectively. The standard error of the mean is

Accepted Answer

A)  1.875 
B)  40 
C)  5 
D)  15

Question 8

The set of all elements of interest in a study is

Accepted Answer

A)  set notation 
B)  a set of interest 
C)  a sample 
D)  a population

Question 9

A population has a mean of 80 and a standard deviation of 7. A sample of 49 observations will be taken. The probability that the sample mean will be larger than 82 is

Accepted Answer

A)  0.5228 
B)  0.9772 
C)  0.4772 
D)  0.0228

Question 10

Random samples of size 81 are taken from an infinite population whose mean and standard deviation are 200 and 18, respectively. The distribution of the population is unknown. The mean and the standard error of the mean are

Accepted Answer

A)  200 and 18 
B)  81 and 18 
C)  9 and 2 
D)  200 and 2

Question 11

Exhibit 7-3
In a local university, 40% of the students live in the dormitories. A random sample of 80 students is selected for a particular study.
-Refer to Exhibit 7-3. The probability that the sample proportion the proportion living in the dormitories) is at least 0.30 is

Accepted Answer

A)  0.4664 
B)  0.9328 
C)  0.9664 
D)  0.0336

Question 12

There are 500 employees in a firm, 45% are female. A sample of 60 employees is selected randomly.
a. Determine the standard error of the proportion.
b. What is the probability that the sample proportion proportion of females) is between 0.40 and 0.55?

Accepted Answer

The answer of There are 500 employees in a firm,...

Question 13

As the sample size increases, the variability among the sample means

Accepted Answer

A)  increases 
B)  decreases 
C)  remains the same 
D)  depends upon the specific population being sampled

Question 14

Consider a population of five weights identical in appearance but weighing 1, 3, 5, 7, and 9 ounces.
a. Determine the mean and the variance of the population.
b. Sampling without replacement from the above population with a sample size of 2 produces ten possible samples. Using the ten sample mean values, determine the mean of the population and the variance of .
c. Compute the standard error of the mean.

Accepted Answer

The answer of Consider a population of five weights identical...

Question 15

The standard deviation of a point estimator is called the

Accepted Answer

A)  standard deviation 
B)  standard error 
C)  point estimator 
D)  variance of estimation

Question 16

A population has a mean of 84 and a standard deviation of 12. A sample of 36 observations will be taken. The probability that the sample mean will be between 80.54 and 88.9 is

Accepted Answer

A)  0.0347 
B)  0.7200 
C)  0.9511 
D)  8.3600

Question 17

A simple random sample of size n from an infinite population of size N is to be selected. Each possible sample should have

Accepted Answer

A)  the same probability of being selected 
B)  a probability of 1/n of being selected 
C)  a probability of 1/N of being selected 
D)  a probability of N/n of being selected

Question 18

An experimental diet to induce weight loss was followed for one week by a randomly selected group of 12 students with the following results.
 $\begin{array}{cc}\text { student }&\text { Loss in Pounds }\
1 & 2.2 \
2 & 2.6 \
3 & 0.4 \
4 & 2.0 \
5 & 0.0 \
6 & 1.8 \
7 & 5.2 \
8 & 3.8 \
9 & 4.2 \
10 & 3.8 \
11 & 1.4\
12&2.6
\end{array}$ 
a. Find a point estimate for the average amount lost after one week on this diet. Is this an unbiased estimate of the population mean? Explain.
b. Find a point estimate for the variance of the amount lost on this diet. Is this an unbiased estimate of the population variance? Explain.
c. Find a point estimate for the standard deviation of the amount lost on this diet.

Accepted Answer

The answer of An experimental diet to induce weight loss...

Question 19

There are 8,000 students at the University of Tennessee at Chattanooga. The average age of all the students is 24 years with a standard deviation of 9 years. A random sample of 36 students is selected.
a. Determine the standard error of the mean.
b. What is the probability that the sample mean will be larger than 19.5?
c. What is the probability that the sample mean will be between 25.5 and 27 years?

Accepted Answer

The answer of There are 8,000 students at the University...

Question 20

A population has a mean of 300 and a standard deviation of 18. A sample of 144 observations will be taken. The probability that the sample mean will be between 297 to 303 is

Accepted Answer

A)  0.4332 
B)  0.8664 
C)  0.9332 
D)  0.0668

Exam 7: Sampling and Sampling Distributions