STAT 102 Quiz 1

The Central Limit Theorem is important in statistics because:

• for any size sample, it says the sampling distribution of the sample mean is approximately normal

• for any population, it says the sampling distribution of the sample mean is approximately normal,

  regardless of the sample size

• for a large n, it says the population is approximately normal

• for a large n, it says the sampling distribution of the sample mean is approximately normal, regardless of

  the population

Which of the following statements about the sampling distribution of the sample mean is incorrect?

• The sampling distribution is generated by repeatedly taking samples of size n and computing the sample

  means.

• The standard deviation of the sampling distribution is σ.

• The sampling distribution is approximately normal whenever the sample size is sufficiently large (n ≧ 30).

• D) The mean of the sampling distribution is μ.

As the sample size gets larger, the standard error of the sampling distribution of the sample mean gets larger as well.

• TRUE

• FALSE

The Central Limit Theorem guarantees that the population is normal whenever n is sufficiently large.

• TRUE

• FALSE

A study was conducted to determine what proportion of all college students considered themselves as full-time students. A random sample of 300 college students was selected and 210 of the students responded that they considered themselves full-time students. Which of the following would represent the target parameter of interest?

• μ

• p

• 233%

• 67%

• 98%

• 78%

A 90% confidence interval for the mean percentage of airline reservations being canceled on the day of the flight is (1.1%, 3.2%). What is the point estimator of the mean percentage of reservations that are canceled on the day of the flight?

• 1.05%

• 2.15%

• 2.1%

• 1.60%

The real estate industry claims that it is the best and most effective system to market residential real estate. A survey of randomly selected home sellers in Illinois found that a 95% confidence interval for the proportion of homes that are sold by a real estate agent is 69% to 81%. Interpret the interval in this context.

• In 95% of the years, between 69% and 81% of homes in Illinois are sold by a real estate agent.

• 95% of all random samples of home sellers in Illinois will show that between 69% and 81% of homes are

  sold by a real estate agent.

• We are 95% confident that between 69% and 81% of homes in this survey are sold by a real estate agent.

• We are 95% confident, based on this sample, that between 69% and 81% of all homes in Illinois are sold by

  a real estate agent.

• If you sell a home in Illinois, you have an 75% ± 6% chance of using a real estate agent.

The real estate industry claims that it is the best and most effective system to market residential real estate. A survey of randomly selected home sellers in Illinois found that a 99% confidence interval for the proportion of homes that are sold by a real estate agent is 70% to 80%. Explain what "99% confidence" means in this context.

• In 99% of the years, between 70% and 80% of homes in Illinois are sold by a real estate agent.

• About 99% of all random samples of home sellers in Illinois will produce a confidence interval that

  contains the true proportion of homes sold by a real estate agent.

• There is a 99% chance that the true proportion of home sellers in Illinois who sell their home with a real estate agent is between 70% and 80%.

• 99% of home sellers in Illinois will sell their home with a real estate agent between 70% and 80% of the

  time.

• About 99% of all random samples of home sellers in Illinois will find that between 70% and 80% of homes are sold by a real estate agent.

An educator wanted to look at the study habits of university students. As part of the research, data was collected for three variables - the amount of time (in hours per week) spent studying, the amount of time (in hours per week) spent playing video games and the GPA - for a sample of 20 male university students. As part of the research, a 95% confidence interval for the average GPA of all male university students was calculated to be: (2.95, 3.10). Which of the following statements is true?

• In construction of the confidence interval, a t-value with 20 degrees of freedom was used.

• In construction of the confidence interval, a z-value was used.

• In construction of the confidence interval, a t-value with 19 degrees of freedom was used.

• In construction of the confidence interval, a z-value with 20 degrees of freedom was used.