ECO 251 - CLT
According to a report by Capital Economics, the average monthly mortgage payment in Chicago is $1,002. Assume that the standard deviation for monthly mortgage payments in Chicago is $168. To confirm these results, a random sample of 55 homeowners in Chicago was selected and found to have an average monthly mortgage payment of $1,030. Do the results of this survey support the report by Capital Economics?
$1,046.37 - $957.63 Because 1,030 is between these limits, the results of this survey do support the report by Capital Economics.
According to the Kaiser Family Foundation, the average annual premium paid by workers with employee-provided health insurance for family coverage was $4,129 in a recent year. Assume that the standard deviation for this annual premium is $560. To confirm these results, a random sample of 42 households with employee-provided health insurance was collected and found to have an average premium of $4,470 for family coverage. Determine the interval that contains 95% of the sample means from this sampling distribution and conclude whether or not this sample supports the findings of the Kaiser Family Foundation.
$4,298.36 - $3,959.64 Because the sample mean $4,470 does not fall with this interval, the sample does not support the findings of the Kaiser Family Foundation.
A recent survey found that 86% of employees plan to devote at least some work time to follow games during the NCAA Men's Basketball Tournament. A random sample of 100 employees was selected. What is the probability that less than 80% of this sample will devote work time to follow games?
0.0418
According to a recent Catalyst Census, 16% of executive officers were women with companies that have company headquarters in the Midwest. A random sample of 125 executive officers from these companies was selected. What is the probability that more than 20% of this sample is comprised of female employees?
0.1112
According to Nielsen, the average smartphone owner used 606 megabytes of data per month. Assume that the standard deviation of data usage was 240 megabytes per month. A random sample of 60 smartphone users was selected. What is the probability that the average amount of data used in this sample was less than 580 megabytes?
0.2005
According to the Labor Department, the average duration of unemployment for adults ages 20 to 24 was 34.6 weeks during a recent month. Assume that the standard deviation for this population is 10.2 weeks. A random sample of 36 adults in this age group was selected. What is the probability that the average duration of unemployment was between 31 and 35 weeks?
0.5778
According to the National Retail Federation, men spent an average of $484 over a recent Black Friday weekend. Assume that the standard deviation for this population is $146. A random sample of 42 men shoppers over this weekend was selected. What is the probability that the average amount spent on Black Friday weekend from this sample was less than $500?
0.7611
According to the National Retail Federation, women spent an average of $317 over a recent Black Friday weekend. Assume that the standard deviation for this population is $90. A random sample of 50 women shoppers over this weekend was selected. What is the probability that the average amount spent on Black Friday weekend from this sample was more than $300?
0.9099
Late flights for U.S. airlines are defined as those arriving 15 minutes later than the scheduled arrival. According to the Department of Transportation, 20.4% of domestic flights were late in a recent year. A random sample of 140 random domestic flights was selected. What is the probability that 35 or fewer flights from this sample were late?
0.9115
According to Strategic Vision, the average age of Mercedes buyers in the U.S. is 54 years old. Assume that the standard deviation for the age of these buyers is 8.5 years. A random sample of 38 Mercedes buyers was selected. What is the probability that the average age of these buyers is less than 56 years old?
0.9265
According to CTIA, the U.S. wireless industry handles more subscribers than any other country in the world, averaging 793 minutes per month per customer. Assume that the standard deviation for the number of minutes used per customer per month is 270. To confirm these results, a random sample of 65 wireless customers was selected and found to have a sample average of 822 minutes. Determine the interval that contains 95% of the sample means from this sampling distribution and conclude whether or not this sample supports the findings of CTIA.
858.6 minutes - 727.4 minutes Because the sample mean falls with this interval, the sample does support the findings of CTIA.
________ errors can occur as a result of a questionnaire that contains ambiguous questions. A) Nonsampling B) Sampling C) Nonprobability D) Judgment
A) Nonsampling
The Central Limit Theorem requires ___________________________________________. A) a sample size of at least 30 be used to ensure that the samples means are normally distributed B) the population be normally distributed to ensure that the samples means are normally distributed C) the bootstrap method to be used to select the sample D) the resampling technique to be used to select the sample
A) a sample size of at least 30 be used to ensure that the samples means are normally distributed
As the size of the sample increases, the _______________________________. A) standard error of the mean becomes smaller B) population standard deviation increases C) sampling error increases D) shape of the sampling distribution becomes wider
A) standard error of the mean becomes smaller
In ________ sampling, we divide the population into mutually exclusive groups and randomly sample from each of these groups. A) stratified B) cluster C) probability D) simple random
A) stratified
A ________ sample is used when members of the population are chosen to become part of the sample simply because they are easily accessible. A) cluster B) convenience C) probability D) stratified
B) convenience
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 when the sample size is sufficiently large C) population distribution for any sample size D) sampling distribution for any sample size
B) sampling distribution when the sample size is sufficiently large
A ________ sample is a sample in which every member of the population has an equal chance of being chosen. A) systematic B) simple random C) probability D) stratified
B) simple random
The sampling distribution of the proportion follows the ________ probability distribution. A) Poisson B) uniform C) binomial D) exponential
C) binomial
A ________ sample is a sample in which each member of the population has a known, nonzero, chance of being selected for the sample. A) systematic B) simple random C) probability D) convenience
C) probability
The statistical technique where many samples are repeatedly drawn from a population is known as ____________. A) convenience sampling B) nonprobability sampling C) resampling D) probability sampling
C) resampling
The process of recording information from the entire population is known as ______________. A) collecting a sample B) resampling C) a bootstrap D) a census
D) a census
A population mean is an example of a statistic.
FALSE
A common source of nonsampling errors is a survey that contains ambiguous questions in the eyes of the respondent.
TRUE
A convenience sample is an example of a nonprobability sample.
TRUE
A sample median is an example of a statistic.
TRUE
A small sample size could provide a smaller sampling error than a larger sample size when taken from the same population.
TRUE
An Internet poll, where individuals may respond to a survey as many times as they choose to, is an example of a nonprobability sample.
TRUE
Cluster sampling is often used to test market new products.
TRUE
Sampling error is the difference between a sample statistic and a population parameter.
TRUE
Sampling without replacement means that once a member of a population is chosen for a sample, it cannot be chosen again for the same sample.
TRUE
The sample means for a population that follows the normal distribution will also be normally distributed, regardless of the size of the samples.
TRUE
The sampling distribution of the proportion describes the pattern that sample proportions tend to take on when randomly drawn from a population.
TRUE
The sampling error for a census equals zero.
TRUE
The standard error of the mean is the sample mean standard deviation, which measures the variation around the mean of the sample means.
TRUE
We expect the average value of many sample means to be close to the population mean from which they were drawn.
TRUE