exam 2
Suppose you take a random sample of size 25 from a population where the population proportion is 0.5. What is the expected value of the sample proportion?
0.5
Suppose the population mean is 70 and the standard error of the mean is 5. What is the z-score associated with a sample mean of 80?
2
The population proportion is 0.6. In a random sample from the population, you find a sample proportion of 0.64. The sampling error is _____.
0.04
Suppose you take a random sample of size 25 from a population where the population proportion is 0.5. What is the standard error of the proportion?
0.1
The sampling distribution of the proportion approximately follows the normal distribution when the values np and n(1-p) are greater than or equal to _____. a.30 b.5 c.20 d.50
b
Which of the following distributions would have the widest spread? a. mu = 10, s=1 b. mu=0, s=0.5 c. mu=5, s=2 d. mu=0, s=5
d
The sample variance is a random variable. True or False
true
Assuming income is normally distributed, what is the probability that? x - = 41,397 a. 0.0 b. 1.0 c. not enough information to know
a
If we are calculating a 99% confidence interval, how much area (probability) is in the upper tail? a. 0.005 b. 0.010 c. 0.990 d. 0.10
a
Suppose that p ¯ = .19 and n = 1000. What is the 95% confidence interval for the population proportion p? a. (0.166, 0.214) b. (0.178, 0.202) c. (0.05, 0.95)
a
Suppose the population mean is 70 and the standard error of the mean is 5. What is the range of sample means within 10 of the population mean?
(60,80)
Suppose the population proportion is 0.5 and the standard error of the proportion is 0.1. What is the z-score associated with a sample proportion of 0.47?
-0.3
The average age of the MBA students in a statistics class is 30.7 years old. The ages of five randomly selected students from the class are: 36, 25, 25, 29, 30. What is the sampling error?
-1.7 years
What is the standard error of the mean?
The standard deviation of the sampling distribution of x -
What is the main benefit of a larger sample size?
There is a higher probability that the sample mean falls within a specified distance from the population mean
The sampling distribution of the sample mean _____. a. is the probability distribution showing all possible values of the sample mean b. is used as a point estimator of the population mean mu c. is an unbiased estimator d. shows the distribution of all possible values of mu
a
To save money, you are forced to use a sample of 10 observations rather than 25. The confidence intervals for n = 10 will be a. wider than confidence intervals for n = 25 b. the same width as the confidence intervals for n=25 c. narrower than the confidence intervals for n=25
a
When a variable follows a continuous distribution, what is the probability of one specific value occurring? a. 0.00 b. 0.50 c. 1.00 d. Depends on the value
a
Which of the following statements is not true regarding the characteristics of the Student's t-distribution? a. it is bell-shaped and symmetrical around the mean of the distribution b. the area under the curve is equal to 1.0 c. As the degrees of freedom increases, the shape of the Student's t-distribution becomes similar to the normal distribution. d. The shape of the Student's t-distribution is narrower than the size of the normal distribution
d
A parameter is a characteristic of a sample. True or False
false
What happens as the sample size increases?
sample of error decreases
Under random sampling, the probability distribution of the population mean is its sampling distribution. True or false
false
Sampling bias occurs when the sample is _______ of the population.
not representative
Random sampling with and without replacement are very similar when the sample size is ____ relative to the population size.
small
In a random sample of 16 observations, the variance of the sample mean is 4 times ____ than the population variance.
smaller
Suppose the population proportion is 0.84, and you want to know the probability of obtaining a sample proportion within 0.04 of the population proportion. What range are you considering?
(0.80,0.88)
Consider a population with a mean of 20 and a standard deviation of 3. You take a sample of size 36. What is the standard error of the mean?
1/2
Consider a population with a mean of 20 and a standard deviation of 3. You take a sample of size 36. What is the expected value of the sample mean?
20
Suppose you sample 2 observations out of a population of 5. If you sample with replacement, the total number of possible samples is ___.
25
Suppose you have a population of 3 children with heights of 36, 50, and 52 inches. You select a random sample of 2 children. The expected value of x ¯ (x bar) is ____
46 inches
An 80% confidence interval will be a. wider than a 95% confidence interval b. narrower than a 95% confidence interval c. the same width as a 95% confidence interval
b
An increase in the population standard deviation ______________ the width of confidence intervals. a. decreases b.increases c. has no effect on
b
Suppose that n=20 and we are constructing an 95% confidence interval. What t score do we use? a. 1.96 b. 2.093 c. 1.729 d. 2.086
b
Suppose that p ¯ = 0.5 and n=25. What is s_{p} a. 0.01 b. 0.10 c. 1.0 d. 0.1414
b
A _______________ sample is used when members of the population are chosen to become part of the sample because they are easily accessible. a. stratified b. probability c. convenience d. cluster
c
If the middle area is 0.90, what are the relevant z-scores? a. 1.96 b. 1.00 c. 1.645
c
If we don't know the population standard deviation, when can we use a normal distribution instead of a t-distribution? a. never; we always must use the normal distribution b. when n is greater than or equal to 10 c. when n is greater than or equal to 30 d. when n is greater than or equal to 100
c
If we had 1,000 samples and were constructing a 90 percent confidence interval, how many confidence intervals would we expect to include the population mean? a. 90 b. 0.9 c. 900 d. 95
c
If you are constructing a 90 percent confidence interval, what is the level of significance? a. 0.9 b. 90% c. 0.10 d. 0.05
c
The Central Limit Theorem plays an important role in statistics because it provides information about the shape of the ______. A. Population distribution when the sample size is sufficiently large b. Sampling distribution for any sampling size c. sampling distribution when the sample size is sufficiently large d. population distribution for any sample size
c
Suppose that Apple is conducting a survey of potential iPad users. Management believes that a person's gender could affect a respondent's answers. What type of sampling would ensure that the sample was composed of an equal number of male and female respondents? a. convenience b. cluster c. simple random d. stratified
d
Suppose that n=10 and we are constructing an 80% confidence interval. What t score do we use? a. 1.372 b. we don't know - there is no 0.8 column in the table c. 1.812 d. 1.383
d
increasing the sample size when calculating a confidence interval while keeping the confidence level constant will ____. a. increase the margin of error resulting in a wider confidence interval b. reduce the margin of error resulting in a wider confidence interval c. increase the margin of error resulting in a narrower confidence interval d. reduce the margin of error resulting in a narrower confidence interval
d
Suppose that for the population of UNCG students, the mean of GPA is 3.46 and the median of GPA is 3.02. If you randomly select a student from the population, the expected value of his or her GPA is _____.
equal to 3.46
A population parameter varies from one sample to the next. True or False
false
In stratified sampling, an observation can belong to multiple strata. True or false
false
Sampling error occurs when the procedure used to select the random sample is not correct. True or False
false
Suppose you have two samples. Sample A was collected using probability and sample B was collected without using probability. Then sample A is representative and sample B is not. True or false
false
Suppose you want to figure out the average number of credit hours among UNCG students. A sample of sophomores is a representative sample for your analysis. True or false
false
The population distribution is the probability distribution of the population parameters. True or false
false
The sampling distribution is the probability distribution of the sample. True or false
false
True or false? A sample size of 18 is considered large enough to apply the Central Limit Theorem.
false
True or false? Unlike the sample mean, increasing the sample size does not help us get a sample proportion closer to the population proportion.
false
The Central Limit Theorem states that the sampling distribution of x ¯ is normally distributed as long as __________.
the sample size is large enough
In a simple random sample all observations in the population are equally likely to end up in the sample. True or false
true
The sample median is a point estimate of the population median. True or False
true
True or false? To calculate a z-score for a sample mean, you need to calculate the standard error of the mean.
true
True or false? We can usually approximate the sampling distribution of LaTeX: \bar{p} p ¯ with the normal distribution.
true
When sampling without replacement, the same observation cannot be selected into your sample multiple times. True or false
true
Suppose you take a random sample of size 25 from a population where the population proportion is 0.5. Can we approximate the sampling distribution of p ¯ with the normal distribution?
yes