stats exam 2

Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a certain year in the past. Suppose a sample of 100 major league players was taken. What was the standard error for the sample mean salary?

$0.12 million

If the expected value of a sample statistic is equal to the parameter it is estimating, then we call that sample statistic

unbiased.

Sampling distributions describe the distribution of

statistics.

Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a certain year in the past. Suppose a sample of 100 major league players was taken. Find the approximate probability that the mean salary of the 100 players was no more than $3.0 million.

z= 3.0-3.26/(1.2/100) = -2.1667 0.0914

Which of the following is true about the sampling distribution of the sample mean?

The mean of the sampling distribution is always μ .

True or False: A sampling distribution is a distribution for a statistic

true

The mean score of all pro golfers for a particular course has a mean of 70 and a standard deviation of 3.0. Suppose 36 pro golfers played the course today. Find the probability that the mean score of the 36 pro golfers exceeded 71. _____________

* how to calculate Z value * z = 71-70 / (3/ *square root of 36) = 1/3/6 ) = 1/.5=2 .9772 1-.9772=.0028

Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a certain year in the past. Suppose a sample of 100 major league players was taken. Find the approximate probability that the mean salary of the 100 players exceeded $3.5 million.

0.0228

At a computer manufacturing company, the actual size of a particular type of computer chips is normally distributed with a mean of 1 centimeter and a standard deviation of 0.1 centimeter. A random sample of 12 computer chips is taken. What is the standard error for the sample mean?

0.029

At a computer manufacturing company, the actual size of a particular type of computer chips is normally distributed with a mean of 1 centimeter and a standard deviation of 0.1 centimeter. A random sample of 12 computer chips is taken. What is the probability that the sample mean will be below 0.95 centimeters? ________________

0.0418

The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, with mean of 3.2 pounds and standard deviation of 0.8 pound. If a sample of 16 fish is taken, what would the standard error of the mean weight equal?

0.200

A manufacturer of power tools claims that the mean amount of time required to assemble their top-of-the-line table saw is 80 minutes with a standard deviation of 40 minutes. Suppose a random sample of 64 purchasers of this table saw is taken. The probability that the sample mean will be less than 82 minutes is __________.

0.6554

manufacturer of power tools claims that the mean amount of time required to assemble their top-of-the-line table saw is 80 minutes with a standard deviation of 40 minutes. Suppose a random sample of 64 purchasers of this table saw is taken. The probability that the sample mean will be greater than 88 minutes is __________.

25. 0.0548

standard error of the mean

All of the above

For air travelers, one of the biggest complaints is of the waiting time between when the airplane taxis away from the terminal until the flight takes off. This waiting time is known to have a right skewed distribution with a mean of 10 minutes and a standard deviation of 8 minutes. Suppose 100 flights have been randomly sampled. Describe the sampling distribution of the mean waiting time between when the airplane taxis away from the terminal until the flight takes off for these 100 flights

Distribution is approximately normal with mean = 10 minutes and standard error = 0.8 minutes.

Why is the Central Limit Theorem so important to the study of sampling distributions?

It allows us to disregard the shape of the population when n is large.

Sales prices of baseball cards from the 1960s are known to possess a right skewed distribution with a mean sale price of $5.25 and a standard deviation of $2.80. Suppose a random sample of 100 cards from the 1960s is selected. Describe the sampling distribution for the sample mean sale price of the selected cards.

Normal with a mean of $5.25 and a standard error of $0.28

Suppose the ages of students in Statistics 101 follow a right skewed distribution with a mean of 23 years and a standard deviation of 3 years. If we randomly sampled 100 students, which of the following statements aboutthe sampling distribution of the sample mean age is incorrect

The standard deviation of the sampling distribution is equal to 3 years.

The Central Limit Theorem is important in statistics because

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

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

the standard deviation of the sampling distribution of the sample mean is equal to σ .

True or False: The Central Limit Theorem ensures that the sampling distribution of the sample mean approaches a normal distribution as the sample size increases.

true

True or False: The Central Limit Theorem is considered powerful in statistics because it works for any population distribution provided the sample size is sufficiently large and the population mean and standard deviation are known.

true

True or False: The standard error of the mean is also known as the standard deviation of the sampling distribution of the sample mean.

true