Stats Exam #3 8,9,10
Consider the statement: 'The distribution of the mean weight of the sampled cans of Ocean brand tuna is Normal.'
It is a correct statement, but it is not a result of the Central Limit Theorem.
The weights of cans of Ocean brand tuna are supposed to have a net weight of 6 ounces. The manufacturer tells you that the net weight is actually a Normal random variable with a mean of 5.95 ounces and a standard deviation of 0.2 ounces. Suppose that you draw a random sample of 42 cans. Part i) Suppose the number of cans drawn is doubled. How will the standard deviation of the sample mean weight change?
. It will decrease by a factor of √2.
𝑥⎯⎯⎯±1.96(𝜎𝑛√)
95%
What is a confidence statement a statement about?
A confidence interval is a statement about the population mean, not the sample mean or individual observations.
Consider the statement: 'The distribution of the mean printing speed of the sampled printers is Normal.'
Correct, but not due to the Central Limit Theory
Increasing the sample size while keeping the same confidence level has what effect on the margin of error?
Decreases the margin of error and hence increases the precision
The mean of the sampling distribution is_______the mean of the population. '' GREATER THAN '', '' EQUAL TO '', '' LESS THAN '', or '' NOT ENOUGH INFORMATION '',
Equal to
Increasing the confidence level while keeping the same sample size has what effect on the margin of error?
Increases the margin of error and hence decreases the precision
An HP laser printer is advertised to print text documents at a speed of 18 ppm (pages per minute). The manufacturer tells you that the printing speed is actually a Normal random variable with a mean of 17.57 ppm and a standard deviation of 3 ppm. Suppose that you draw a random sample of 11 printers. Part i) Suppose the number of printers drawn is quadrupled. How will the standard deviation of the sample mean printing speed change?
It will decrease by a factor of 2.
Suppose the number of printers drawn is quadrupled. How will the mean of the sample mean printing speed change?
It will remain unchanged.
The weights of cans of Ocean brand tuna are supposed to have a net weight of 6 ounces. The manufacturer tells you that the net weight is actually a Normal random variable with a mean of 5.95 ounces and a standard deviation of 0.2 ounces. Suppose that you draw a random sample of 42 cans. Suppose the number of cans drawn is doubled. How will the mean of the sample mean weight change?
It will remain unchanged.
The standard deviation of the sampling distribution is_______the standard deviation of the population Greater than, equal to, less then or not enough info
Less than
Holding everything else constant, which change to the sample size will reduce the width of a confidence interval for a population mean by half?
Quadruple the sample size.
Suppose you collect a SRS of size n from a population and from the data collected you computed a 95% confidence interval for the mean of the population. Which of the following would produce a new confidence interval with larger width (larger margin of error) based on these same data?
Use a larger confidence level.
A 95% confidence interval for the mean 𝜇μ of a population is computed from a random sample and found to be 10±410±4. We may conclude
that if we took many, many additional samples and from each computed a 95% confidence interval for 𝜇μ, approximately 95% of these intervals would contain 𝜇μ.