Stat Midterm 2
Random samples of size 49 are taken from an infinite population whose mean is 300 and standard deviation is 21. The mean and standard error of the sample mean, respectively, are:
300 and 3
A sample of size 25 is selected at random from a finite population. If the finite population correction factor is 0.63, then the population size is:
41
The expected value of the sampling distribution of the sample mean equals the population mean μ :
for all populations
Random samples of size 81 are taken from an infinite population whose mean and standard deviation are 45 and 9, respectively. The mean and standard error of the sampling distribution of the sample mean are:
45 and 9/(sq81)
In developing an interval estimate for a population mean, the population standard deviation σ was assumed to be 10. The interval estimate was 50.92 ± 2.14. Had σ equaled 20, the interval estimate would be
50.92 ± 4.28
Suppose an interval estimate for the population mean was 62.84 to 69.46. The population standard deviation was assumed to be 6.50, and a sample of 100 observations was used. The mean of the sample was:
66.15
A major electronics store chain is interested in estimating the average amount its credit card customers spent on their first visit to the chain's new store in the mall. Fifteen credit card accounts were randomly sampled and analyzed with the following results: = $50.50 and s2 = 400. A 95% confidence interval for the average amount the credit card customers spent on their first visit to the chain's new store in the mall is:
$50.50 ± $11.08.
The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, with a mean of 3.2 pounds and standard deviation of 0.84 pounds. If a sample of 16 fish is taken, what is the standard error of the mean weight?
0.210
Given an infinite population with a mean of 75 and a standard deviation of 12, the probability that the mean of a sample of 36 observations, taken at a random from this population, is less than 78 is:
0.9332
The value for a 95% confidence interval estimate for a population mean μ is
1.96
An infinite population has a mean of 40 and a standard deviation of 15. A sample of size 100 is taken at random from this population. The standard error of the sample mean equals:
15/(sq100)
In developing an interval estimate for a population mean, a sample of 50 observations was used. The interval estimate was 19.76 ± 1.32. Had the sample size been 200 instead of 50, the interval estimate would have been:
19.76 ± .66
The owner of a meat market has an assistant who has determined that the weights of roasts are normally distributed, with a mean of 3.2 pounds and standard deviation of 0.8 pounds. If a sample of 25 roasts yields a mean of 3.6 pounds, what is the Z-score for this sample mean?
2.50
For a 99% confidence interval of the population mean based on a sample of n = 25 with s = 0.05, the critical value of t is:
2.7969
If all possible samples of size n are drawn from an infinite population with a mean of 15 and a standard deviation of 5, then the standard error of the sample mean equals 1.0 for samples of size:
25
Consider an infinite population with a mean of 160 and a standard deviation of 25. A random sample of size 64 is taken from this population. The standard deviation of the sample mean equals:
25/(sq64)
A random sample of size 15 taken from a normally distributed population revealed a sample mean of 75 and a sample variance of 25. The upper limit of a 95% confidence interval for the population mean would equal:
77.77
The standard error of the mean:
All of the choices are true
A 99% confidence interval estimate of the population mean μ can be interpreted to mean:
All of these choices
The width of a confidence interval estimate of the population mean increases when the:
All of these choices
Suppose that 100 items are drawn from a population of manufactured products and the weight, X, of each item is recorded. Prior experience has shown that the weight has a non-normal probability distribution with μ = 8 ounces and σ = 3 ounces. Which of the following is true about the sampling of ?
All of these choices are true
Researchers determined that 60 Puffs tissues is the average number of tissues used during a cold. Suppose a random sample of 100 Puffs users yielded the following data on the number of tissues used during a cold: = 52 and s = 22. Suppose the test statistic does not fall in the rejection region at α = 0.05. Which of the following conclusions is correct?
At α = 0.05, we do not reject H0.
Which of the following is an incorrect statement about a 90% confidence interval?
If we repeatedly draw samples of the same size from the same population, 90% of the resulting confidence intervals will include μ.
Suppose a 95% confidence interval for μ turns out to be (1,000, 2,100). What does it mean to be 95% confident?
In repeated sampling, the population parameter would fall in the resulting interval 95% of the time.
After computing a confidence interval, the user believes the results are meaningless because the width of the interval is too large. Which one of the following is the best recommendation?
Increase the sample size
After constructing a confidence interval estimate for a population mean, you believe that the interval is useless because it is too wide. In order to correct this problem, you need to:
Increase the sample size
The Central Limit Theorem states that, if a random sample of size n is drawn from a population, then the sampling distribution of the sample mean :
Is approx. normal if n>30
Which of the following is true regarding the sampling distribution of the mean for a large sample size? Assume the population distribution is not normal.
It has the same mean as the population, but a different shape and standard deviation
Suppose X has a distribution that is not normal. The Central Limit Theorem is important in this case because:
It says the sampling distribution of is approx. normal if n is large enough
Which of the following statements about the sampling distribution of is NOT true?
Its standard deviation is equal to the population standard deviation σ
The value added and subtracted from a point estimate in order to develop an interval estimate of the population parameter is known as the
Margin of error
The level of significance is the
Maximum allowable probability of Type I error
In the formula , the α / 2 refers to:
None of these choices
The letter α in the formula for constructing a confidence interval estimate of the population mean is:
None of these choices
Which of the following is true about the sampling distribution of the sample mean?
None of these choices
The standard error of the mean for a sample of 100 is 25. In order to cut the standard error of the mean in half (to 12.5) we must:
None of these choices are true
If a random sample of size n is drawn from a normal population, then the sampling distribution of the sample mean will be:
Normal for all values of n
For a sample size of 1, the sampling distribution of the mean is normally distributed:
Only if the population is normally distributed
A sample of size 40 is taken from an infinite population whose mean and standard deviation are 68 and 12, respectively. The probability that the sample mean is larger than 70 equals
P(Z>0.17)
Which of the following conditions does not allow you to use the formula to estimate μ?
Population has any distribution and n is any size.
For sample sizes greater than 30, the sampling distribution of the mean is approximately normally distributed:
Regardless of the shape of the population
The level of significance in hypothesis testing is the probability of
Rejecting a true null hypothesis
As a general rule in computing the standard error of the sample mean, the finite population correction factor is used only if the:
Sample size is greater than 5% of the sample size
Sampling distributions describe the distributions of:
Sample statistics
The standard deviation of the sampling distribution is also called the:
Standard error of the sample mean
Suppose the ages of students in your program follow a positively skewed distribution with mean of 24 years and a standard deviation of 4 years. If we randomly sampled 100 students, which of the following statements about the sampling distribution of the sample mean age is NOT true?
The standard deviation of the sampling distribution of sample mean id equal to 4 years
A sample of size n is selected at random from an infinite population. As n increases, which of the following statements is true?
The standard error of the sample mean decreases
Which of the following is not a part of the formula for constructing a confidence interval estimate of the population mean?
The value of the population mean.
The finite population correction factor should be used:
Whenever the sample size is large compared to the population size
It is desired to estimate the average total compensation of CEOs in the publishing industry. Data were randomly collected from 18 CEOs and 95% confidence interval was calculated to be ($2,190,000, $4,720,000). Based on the interval above, do you believe the actual average total compensation of CEOs in the publishing industry could be $3,000,000?
Yes, and I am 95% confident of that.
A confidence interval is defined as:
a lower and upper confidence limit associated with a specific level of confidence.
An interval estimate is a range of values used to estimate
a population parameter
As the number of degrees of freedom for a t distribution increases, the difference between the t distribution and the standard normal distribution
becomes smaller
If all possible samples of size n are drawn from an infinite population with a mean of μ and a standard deviation of σ, then the standard error of the sample mean is inversely proportional to:
blank?
The ability of an interval estimate to contain the value of the population parameter is described by the
confidence level
As the sample size increases, the margin or error
decreases
An estimate of a population parameter that provides an interval of values believed to contain the value of the parameter is known as the
interval estimate
The level of significance
is (1-confidence level)
The degrees of freedom for the test statistic for μ when σ is unknown is:
n − 1
If the confidence level is reduced, the confidence interval:
narrows
A robust estimator is one that is
not sensitive to moderate non-normality.
Researchers determined that 60 Puffs tissues is the average number of tissues used during a cold. Suppose a random sample of 100 Puffs users yielded the following data on the number of tissues used during a cold: = 52 and s = 22. Suppose the alternative we wanted to test was H1: μ < 60. The correct rejection region for α = 0.05 is:
reject H0 if t < −1.6604.
For statistical inference about the mean of a single population when the population standard deviation is unknown, the degrees for freedom for the t-distribution equal n − 1 because we lose one degree of freedom by using the:
sample mean as an estimate of the population mean.
If all possible samples of size n are drawn from a population, the probability distribution of the sample mean is called the:
sampling distribution of
Researchers determine that 60 Puffs tissues is the average number of tissues used during a cold. Suppose a random sample of 100 Puffs users yielded the following data on the number of tissues used during a cold: = 52 and s = 22. Using the sample information provided, the value of the test statistic is:
t = (52 − 60) / (22 / 10)
When s is used to estimate σ, the margin of error is computed by using
t distribution
Whenever the population standard deviation is unknown and the population has a normal or near-normal distribution, which distribution is used in developing an interval estimation?
t distribution
The term 1 − α refers to:
the confidence level.
For the interval estimation of μ when σ is known and the sample is large, the proper distribution to use is
the normal distribution
In hypothesis testing, the tentative assumption about the population parameter is
the null hypothesis
In developing an interval estimate, if the population standard deviation is unknown
the sample standard deviation can be used
In general, higher confidence levels provide
wider confidence intervals
The larger the confidence level, the:
wider the confidence interval.
Based on sample data, the 90% confidence interval limits for the population mean are LCL = 170.86 and UCL = 195.42. If the 10% level of significance were used in testing the hypotheses H0: μ = 201 vs. H1: μ ≠ 201, the null hypothesis:
would be rejected.
