UL MBA - Stats Ch. 9
Place these steps for determining a confidence interval for the population mean, with the population standard deviation not known, in order, first step at the top.
1. Choose a sample size. If the population is known to be normal, a smaller sample will do. 2. Take a sample and find the sample mean and sample standard deviation. 3. Estimate the population standard deviation using the sample standard deviation. 4. Calculate the standard error. 5. Use the appropriate t-value to determine the confidence interval.
What should you do if your calculation for appropriate sample size gives a fractional number?
Round up to the next whole number.
A college has 320 students. The dean checks 50 student records and finds a mean GPA of 2.9 with standard deviation of 0.6. Create a 90% confidence interval for this year's mean GPA. Use the finite population correction factor.
2.769 to 3.031
A large jar contains a mixture of white and black beans. In a randomly chosen handful of 120 beans 40 were black. Create a 95% confidence interval for the proportion of black beans in the jar. Express your answer to the nearest percent.
25% to 42%
What is the effect of the finite population correction factor on a sample based estimate?
It makes the estimate more accurate for larger samples.
How does sample size affect the standard error?
Larger sample size gives a smaller standard error.
For a given confidence level, how does a confidence interval calculated using the t-value compare to one calculated using the z-value?
The confidence interval from the t-value is wider.
What is meant by the the term "Level of Confidence"?
The confidence we feel that a sample has correctly estimated a parameter. The probability that a parameter will be found within the confidence interval.
Which three of the following items are valid considerations in the choice of sample size?
The population dispersion. The desired level of confidence. The margin of error the researcher will tolerate.
The binomial conditions must be met before we can develop a confidence interval for a population proportion. Which two of the following are binomial conditions?
The probability of success is the same for all trials. We can define two outcomes, success and failure.
Knowing the population standard deviation allows us to choose an appropriate sample size for a study. Which two of the following could be used to estimate the population standard deviation?
The sample standard deviation from a pilot study. One sixth of the population range.
In choosing a sample size for a study, we need to know the population standard deviation. Which two of the following could be used to estimate the population standard deviation?
The sample standard deviation from a pilot study. The population standard deviation from a comparable study.
For a specific confidence level how do the t-value and the z-value compare?
The t-value is larger than the z-value.
To develop a confidence interval for a population proportion the binomial conditions must be met. Which of the following is not a requirement?
The trials must be done as sampling without replacement.
True or false: If the formula for sample size gives a fractional value, you should round up to the nearest integer. True False
True
When we want to estimate the mean of a population using a sample, but do not know the population standard deviation, which two of the following steps are required?
Use the sample standard deviation as an estimate of the population standard deviation. Use the t-distribution instead of the Standard Normal to find the confidence interval.
If we are estimating the population mean using a sample, under what circumstances would we use the t-distribution?
When we don't know the population standard deviation.
Which two of the factors listed below determination the width of a confidence interval? a) The chosen level of confidence. b) The population distribution shape. c) The relative size of the sample mean. d) The size of the standard error.
a) The chosen level of confidence. d) The size of the standard error.
Identify three of the following traits that apply to the meaning of "proportion" when used as a statistic.
a) it refers to a fraction, ratio, or percent. b) it can refer to either a sample or a population. c) it identifies a particular trait of interest.
A sample of size 25 taken from a population with standard deviation 6. The sample mean is 10. Which of the following is a 99% confidence interval for the population mean?
6.9 to 13.1
What is a Confidence Interval? Choose the best description.
A range of values, created using a sample, within which a population parameter has a certain probability of occurring.
Which of the following statements is the best definition of a Point Estimate?
A sample statistic that estimates a population parameter.
Two of the following considerations require a larger sample size, and two will permit a smaller sample size. Choose the two that will permit a smaller sample.
A smaller population dispersion. A normally distributed population.
When we speak of an "80% confidence level)", what are we referring to?
An 80% probability that a parameter will be within a specific interval.
In estimating the population mean from a sample, two additional steps are necessary when o is not known. Identify them from the list given here.
Find the t-value for the proper distribution, based on the sample size. Find the sample standard deviation.
Why is it necessary to apply the finite population correction factor when a sample is a significant part of the population?
If a sample is a larger part of the population, it will give a better estimate.