Chapter 9 learn smart

What should you do if your calculation for appropriate sample size gives a fractional number?

Round up to the next whole number.

The central limit theorem tells us which of the following?

The sampling distribution follows the normal probability distribution.

A confidence interval for the population proportion is calculated using the formula p ± z √p(1−p)/n. Match the variables to their description.

p- the sample proportion z- the value associated with the confidence level n- the sample size Pie- the population proportion that is being estimated.

What does the symbols in the formula p=x/n stand for? Match the variables to their description.

p- the sample proportion statistic x- "successes" in the sample n- sample size

Which of the following formulas would you use to construct a confidence interval for the mean with σ sd known?

x̅ ± z σ/ √n

A large jar contains a mixture of white and black beans. In a randomly chosen handful of 120 beans 40 were black. Create a 98% confidence interval for the proportion of black beans in the jar. Express your answer to the nearest percent.

23% to 43% 0.333 +- 2.33 √(0.333)(0.667)/120

A large jar contains a mixture of white and black beans. The population proportion of beans was found to be 0.25. What sample size would be needed to estimate the proportion of black with an error of no more than 0.05 and a confidence level of 95%?

289 n=0.25(0.75)(1.96/0.05) squared

Which of the following statements correctly describe the role of the population standard deviation, σ , in creating a confidence interval for the population mean? Select all that apply.

If σ sd is known, we use it to calculate the confidence interval. If σ sd is not known, we estimate it using the sample standard deviation.

Which one of the following is true about a point estimate?

It is a single value calculated from a sample to estimate a population.

Identify which of the following are traits that apply to the meaning of "proportion." Select all that apply.

It refers to a fraction, ratio, or percent. It can refer to either a sample or a population.

How does sample size affect the width of the confidence interval for the population mean?

Larger sample sizes result in narrow intervals.

Which of the factors listed below determine the width of a confidence interval? Select all that apply.

The chosen level of confidence. Higher confidence requires a wider confidence interval. The size of the standard error. A larger standard error, i.e. larger dispersion or smaller sample, gives a wider interval.

Which of the following items are valid considerations in the choice of sample size? Select all that apply.

The desired level of confidence. The margin of error the researcher will tolerate. The population dispersion.

In choosing a sample size for a study, we need to know the population standard deviation. Which of the following could be used to estimate the population standard deviation? Select all that apply.

The population standard deviation from a comparable study. The sample standard deviation from a pilot 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.

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?

We can define two outcomes, success and failure The probability of success is the same for all trials

The formula for estimating the sample size for a study is n=(zσ/E)^2 . Match the variables to their description

n= size of the sample z=standard normal value for the chosen confidence level σ= the population standard deviation E=the max allowable error

Which of the following is the correct formula for choosing the sample size for an estimate of population proportion?

n=p(1-p)(z/E) squared

When the population standard deviation is know, the confidence interval for the population mean is based on the:

z-statistic

Calculate a 95% confidence interval for a sample mean of 20 with a sample standard deviation of 10 and a sample size of 9. The answer should be accurate to the nearest decimal.

12.31 to 27.69 20 +- 2.306 (10/sqrt(9)) use t-distribution

A sample of size 25 is taken from a normally distributed 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 10+- 2.57(6/ sqrt(25))

Suppose you want to estimate the population mean with 95% confidence with a margin of error of 2. If the estimate of the population standard deviation is 8, what sample size is required?

62 n=(1.96*8/2) squared

The central limit theorem tells us that the sample means follow a normal distribution with mean and standard deviation (i.e. standard error) of . This lets us use z-values to set confidence intervals. Match the confidence levels to the z-values.

68% confidence z=1 95% confidence z=1.96 99% confidence z=2.58

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. e.g. P(a<x<b) = 0.95

A proportion would be especially useful in which one of the following cases?

Estimating the percentage of students who have full-time jobs. Proportions work great for nominal data.

In constructing a confidence interval to estimate the population mean from a sample, which of the following steps are necessary only when σ sd is not known? Select all that apply.

Find the sample standard deviation. Find the t-value for the proper distribution, based on the sample size.