Exam 5: Sampling Distributions

On a chilly spring afternoon,10 lab sections of a statistics class all have full attendance.The 10 lab sections each have the same number of students enrolled in it.A class evaluation is about to be administered to some of the students.It has been decided to first randomly select 3 of the 10 lab sections and then give the evaluation to a simple random sample of one-fourth of the students in those sections.Among the students answering the survey,77% said they enjoy the statistics class.Which statement(s)correctly describe the value 77%?

A population of graduate students at a large university was being studied through the use of a sample survey.The researcher was trying to estimate the mean debt carried by the students through student loans and the proportion of all students that carry a student loan.A stratified random sample of 350 students was selected from the various schools within the university.The sample results showed that 30% held a student loan and the mean debt was $18,450.Which of the following statements is TRUE?

The distribution of the amount of money undergraduate students spend on books for a term is slightly right-skewed,with a mean of $400 and a standard deviation of $80.If a simple random sample of 100 undergraduate students is selected,what is the probability that these students spend,on average,more than $425 on books?

A study,conducted by Jackson et al.and published in the journal Cancer Causes and Control in 2009,examined 33,938 women aged 40 to 84 years old who resided in California and who reported having had a mammogram within the last 2 years.The researchers were interested in characteristics of women who routinely obtain mammograms,as suggested by the American Cancer Society,to detect breast cancer.The table below provides a column that refers to the sample size and provides characteristics of the 33,938 women who were included in the study who reported having had a mammogram. Are the results of the study likely biased toward one race/ethnicity group?

The weights of medium oranges packaged by an orchard are Normally distributed with a mean of 14 ounces and a standard deviation of 2 ounces.Ten medium oranges will be randomly selected from a package.What is the sampling distribution of the sample mean weight of a random sample of 10 medium oranges?

The number of undergraduates at Johns Hopkins University is approximately 2000,while the number at Ohio State University is approximately 40,000.Suppose,instead,that at both schools a simple random sample of about 3% of the undergraduates will be taken.What can we conclude about the sampling variability for the sample proportion from Johns Hopkins as compared to that from Ohio State?

A simple random sample of 50 students is taken from a local community college,which has a total of about 1500 students.Another simple random sample of 50 students is taken from a large state university,which has a total of approximately 20,000 students.The sampled students each answer a one-question survey which reads,"About how many MP3 songs do you own?" The sample average number of MP3 songs owned is calculated for the two sets of students.What can we conclude about the sampling variability in the sample average number of MP3 songs of the students sampled from the small community college as compared to that in the sample average of the students sampled from the large state university?

Birth weights of babies born to full-term pregnancies follow roughly a Normal distribution.At Meadowbrook Hospital,the mean weight of babies born to full-term pregnancies is 7 pounds with a standard deviation of 14 ounces (1 pound = 16 ounces). Dr.Watts (who works at Meadowbrook Hospital)has four deliveries (all for full-term pregnancies)coming up during the night.Assume that the birth weights of these four babies can be viewed as a simple random sample.What is the probability that all four babies will weigh more than 7.5 pounds?

A gasoline tank for a certain car is designed to hold 15 gallons of gas.Suppose that the actual capacity of a randomly selected tank has a distribution that is approximately Normal with a mean of 15.0 gallons and a standard deviation of 0.15 gallons.If a simple random sample of four tanks is selected,and their capacities can be considered independent,what is the probability that all four will hold between 14.75 and 15.10 gallons of gas?

A sample is to be selected from a large population using simple random sampling.The proportion of subjects in the sample that have a given characteristic is to be calculated.Which of the following best describes the sample proportion?

The distribution of the amount of money undergraduate students spend on books for a term is slightly right-skewed,with a mean of $400 and a standard deviation of $80.If a student is selected at random,what is the probability that this student spends more than $425 on books?

A call-in poll conducted by USA Today concluded that Americans love Donald Trump.This conclusion was based on data collected from 7800 calls made by USA Today readers.USA Today reported that of the 7800 calls,6435 calls were supportive of Donald Trump.This results in a percentage of 82.5%.Of the 6435 supportive calls,about half came from female callers.Which value(s)can be labeled as statistics?

A study,conducted by Jackson et al.and published in the journal Cancer Causes and Control in 2009,examined 33,938 women aged 40 to 84 years old who resided in California and who reported having had a mammogram within the last 2 years.The researchers were interested in characteristics of women who routinely obtain mammograms,as suggested by the American Cancer Society,to detect breast cancer.The table below provides a column that refers to the sample size and provides characteristics of the 33,938 women who were included in the study who reported having had a mammogram. What is the value of the statistic, ,that represents the proportion of women in California who have less than a high school education?

A population variable has a distribution with a mean of  = 50 and a variance of ² = 225.From this population a simple random sample of n observations is to be selected and the mean of the sample values calculated.How big must the sample size n be so that the standard deviation of the sample mean is equal to 1.4 (i.e. , = 1.4)?

A free cholesterol screening program is set up in the downtown area during lunch hour.Individuals can walk in and have their cholesterol measured for free.One hundred seventy-three people use the service,and their average cholesterol is 217 mg/dL.The value 217 is an example of _________.

The number of undergraduates at Johns Hopkins University is approximately 2000,while the number at Ohio State University is approximately 40,000.A simple random sample of 50 undergraduates at Johns Hopkins University will be obtained to estimate the proportion of all Johns Hopkins students who feel that drinking is a problem among college students.A simple random sample of 50 undergraduates at Ohio State University will be obtained to estimate the proportion of all Ohio State students who feel that drinking is a problem among college students.What can we conclude about the sampling variability in the sample proportion, ,calculated from the sample at Johns Hopkins as compared to that in the sample proportion from Ohio State?

Let X represent the SAT total score of an entering freshman at University X.The random variable X is known to have a N(1200,90)distribution.Let Y represent the SAT total score of an entering freshman at University Y.The random variable Y is known to have a N(1215,110)distribution.A random sample of 100 freshmen is obtained from each university.Let = the sample mean of the 100 scores from University X,and = the sample mean of the 100 scores from University Y.What is the probability that will be less than 1190?

Birth weights of babies born to full-term pregnancies follow roughly a Normal distribution.At Meadowbrook Hospital,the mean weight of babies born to full-term pregnancies is 7 pounds with a standard deviation of 14 ounces (1 pound = 16 ounces). Rachel is one of Dr.Watts's patients.Rachel had an ultrasound 3 weeks ago and the doctors established that the baby already weighed 7 pounds at that point.She is about to deliver her baby (full term).What is the probability that the baby will be more than 8 pounds?

Suppose you are going to roll a six-sided die 60 times and record ,the proportion of times that an even number (2,4,or 6)is showing.At approximately what value should the sampling distribution of be centered?

Suppose you are going to roll a six-sided die 60 times and record ,the proportion of times that an even number (2,4,or 6)is showing.Suppose you decide to roll the die 200 times instead of 60 times.How will this affect the center and spread of the sampling distribution of ?