Exam 5: Sampling Distributions

A sample of size n is selected at random from a population that has mean  and standard deviation .The sample mean will be determined from the observations in the sample.Which of the following statements about the sample mean is/are TRUE?

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 number of oranges in the sample that weigh more than 14 ounces?

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 four tanks are randomly selected,what is the probability that their average capacity will be between 14.75 and 15.10 gallons?

A news program is doing a report on a controversial court case.Daniel VanHowen is being prosecuted for killing a woman in the park,but all the evidence is circumstantial.Right before sentencing,the TV program decides to poll the TV-viewing audience.They wish to estimate the proportion of all people who think Mr.VanHowen is guilty.They decide to post a question on their Web site and ask the TV-viewing audience to answer it.The TV program decides to announce during the program that these opinions only reflect the TV-viewing,computer-using audience.They close the poll after 10 minutes.They had 2371 responses,of which 1542 think that Mr.VanHowen is guilty.What could the news programs have done to reduce the margin of error of the sample percentage of viewers who think that Mr.VanHowen is guilty?

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). What is the probability that the average weight of the four babies will be more than 7.5 pounds?

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. The proportion of the sample that were Latina is an example of a

The proportion of supermarket customers who do not buy store-brand products is to be estimated.Which of the following scenarios would lead to a sampling distribution of the sample proportion with the lowest variability?

A public opinion poll in Ohio wants to determine whether registered voters in the state approve of a measure to ban smoking in all public areas.They select a simple random sample of 50 registered voters from each county in the state and ask whether they approve or disapprove of the measure.The proportion of registered voters in the state who approve of banning smoking in public areas is an example of _________.

The following histogram shows the distribution of 1000 sample observations from a population with a mean of  = 4 and a variance of ² = 8. Suppose a simple random sample of 100 observations is to be selected from the population and the sample average is calculated.Which of the following statements about the distribution of is/are FALSE?

The proportion of supermarket customers who do not buy store-brand products is to be estimated.Suppose 500 customers are selected from the roughly 20,000 customers who shop at the stores citywide.The sample proportion of supermarket customers who do not buy store-brand products equals 33.5%.Which value(s)can be labeled as statistic(s)?

Binomial distributions represent _______ random variables.

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 parameter,p,that represents the proportion of women in California who have less than a high school education?

Every year around Christmas time,many parents take their children to a mall to have their child's picture taken with Santa.The Centennial Mall management has calculated,based on years of experience,that about 40% of all children cry when they sit on Santa's lap.Suppose 80 children were randomly selected from this year's crowd.Of these 80 children,45% cried.If repeated samples of 80 children were to be selected,what is the center of the sampling distribution of the percentage of sampled children who cry when seated on Santa's lap?

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. Having such a large number of the respondents being white would create _____ variability in their responses.

The scores of individual students on the American College Testing (ACT),a college readiness assessment,have a Normal distribution with a mean of 18.6 and a standard deviation of 6.0.At Northside High,36 seniors take the test.Assume the scores at this school have the same distribution as national scores.What is the sampling distribution of the sample mean score for a random sample of 36 students?

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. The data in the sample size column can be considered

The scores of individual students on the American College Testing (ACT),college readiness assessment,have a Normal distribution with a mean of 18.6 and a standard deviation of 6.0.At Northside High,36 seniors take the test.Assume the scores at this school have the same distribution as national scores.What is the mean of the sampling distribution of the sample mean score for a random sample of 36 students?

Does giving an incentive really work on improving exam scores? For example,consider the following treatments to measure the use of incentives. Treatment 1: No incentive Treatment 2: Incentive given to all Treatment 3: Incentive given only if a certain score is received For this experiment,assume all subjects are seniors at a university.To reduce bias,how should you select the items to use in your study?

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.In a simple random sample of 100 undergraduate students,what is the expected value of the sample mean amount of money spent on books?

Hoping to attract more shoppers,a city is planning to build a new public parking garage downtown.The city plans to pay for the structure through parking fees.The consultant,who is advising the city on this project,has selected a simple random sample of 44 weekdays and calculated the average amount in fees collected from neighboring parking structures.The sample mean was $967.Which of the following scenarios would lead to the smallest margin of error?