Chapter 9: Estimation and Confidence Intervals

When the population standard deviation is known, the confidence interval for the population mean is based on the: Chi-square statistic t-statistic z-statistic F-statistic

z-statistic

What is a confidence interval? Choose the best description. A range of probabilities, constructed with a sample, that describes where a population parameter will occur. A range of values, created using a sample, within a population parameter that has a certain probability of occurring. A range of values used to estimate where the sample statistic is likely to occur

A range of values, created using a sample, within a population parameter that has a certain probability of occurring.

A student found out that out of 100 cars that had passed an intersection 20 were made by Ford. Create a 95% confidence interval for the population proportion of cars made by Ford? 0.26 to 0.54 0.13 to 0.27 10 to 30 0.12 to 0.28

0.12 to 0.28

Suppose you wanted to estimateThe population proportion of international students at your university. If you found from a random sample of 50 students that 13 were international, what would be at the center of a 95% confidence interval for the population proportion? 1.96 13 0.13 26 0.26

0.26

A proportion would be specifically useful in which one of the following cases? Estimating the percentage of students who are full-time jobs. Summarizing the annual percentage growth in an investment. Estimating the starting salary for recent college graduates. Summarizing the wait time for patients to go to the doctor.

Estimating the percentage of students who are full-time jobs.

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 in a confidence level of 95%? 73 385 205 289

289 because, n=0.25(0.75)*(1.96/0.05)^2

Suppose you want to estimate the population mean with a 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 61 60 63

62 because, n=((1.96*8)/2)^2

Which of the following considerations require a large sample size? Select all that apply. A higher level of confidence. A smaller margin on air. A smaller population dispersion. A normal distribution population.

A higher level of confidence. A smaller margin on air.

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? 1/6 of the sample mean. The sample distribution shape. 1/6 of the population range. The sample standard deviation from a pilot study.

1/6 of the population range. The sample standard deviation from a pilot study.

Suppose you want to estimate the population mean with 99% confidence with a margin of error of 2.5. If the estimate of the population standard deviation is 11, what sample size is required? 129 130 131 100

129 because, n=((2.68*11)/2.5)^2

Calculate a 90% confidence interval for a sample mean of 15 with a sample standard deviation of 5 and a sample size of 25. The answer should be accurate to the nearest decimal. 13.36 to 16.65 13.29 to 16.71 14.66 to 15.34 12.94 to 17.06

13.29 to 16.71 because 15+-1.711*(5/square root of 25)

What is the value is used to construct a 98% confidence interval for the population mean when the population standard deviation is known? 2.33 2.87 1.93 1.28

2.33, because 0.9800/2=0.4900; z=2.33 -> 0.4901

Suppose you would like to estimate what proportion of students work full-time. If you have no estimate of the population portion, what sample size would be needed to estimate the proportion with an error of no more than 0.04 in a confidence level of 95%? 426 601 115 1825

601 because, n=0.5(1-0.5)*(1.96/0.04)^2

For a given confidence level, how does a confidence interval calculated using the tea value compared to one calculated using the Z-value? Both confidence intervals are the same in size. The confidence interval from the Z value is wider. For small sample sizes, they are nearly the same. The confidence interval from the T-Value is wider.

The confidence interval from the T-Value is wider.

The central limit theorem tells us which of the following? The sampling distribution follows the normal probability distribution. The distribution of the sample means will be either skewed left or right. The distribution of the sample means will match the distribution of the population.

The sampling distribution follows the normal probability distribution.

Which of the following items are valid considerations in the choice of sample size? Select all that apply. The desired level of confidence. The median population being studied. The population dispersion. The margin of error the researcher will tolerate.

The desired level of confidence. The population dispersion. 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 of the following are binomial conditions? We can find two outcomes, success and failure. The outcomes of one trail are affected by the outcomes of previous trials. The probability of success is the same for all trials. The sample represents the number of successes in a specified time period.

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

If there is no estimate of the population proportion, what value should be used? 0 5 0.5 1

0.5

For a specific confidence level how did the T-Value and The z-value compare? The t-value and the z-value are the same. The Z-value is larger than the t-value. The T-value is larger than the z-value.

The T-value is larger than the z-value.

Which of the factors listed below determine the width of a confidence interval? Select all that apply. The chosen level of confidence. The population mean. The relative size of the sample mean. The size of the standard error.

The chosen level of confidence. The size of the standard error.

In constructing a confidence interval to estimate the population mean from a sample, which of the following steps are necessarily only when standard deviation is not known? Select all that apply. Determine the desired confidence level. Find the sample standard deviation. Find the T-Value for the proper distribution, based on the sample size. Calculate the sample mean.

Find the sample standard deviation. Find the T-Value for the proper distribution, based on the sample size.

Which of the following statements correct we do start describes the role of the population standard deviation, in creating a confidence interval for the population mean? Select all that apply. If standard deviation is not known, we use the range to estimate it from the sample. If standard deviation is known, we use it to calculate the confidence interval. If the standard deviation does not equal us, the sample standard deviation, we will use the smaller of the two values to find the Z value. If the standard deviation is not known, we estimate it using the sample standard deviation.

If standard deviation is known, we use it to calculate the confidence interval. If the standard deviation 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 range of values used to estimate a population parameter. The probability estimate is provided to measure the accuracy of the point estimate. It is a single value calculated from a sample to estimate a population.

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

Identify which of the following are trails that apply to the meaning of "proportion". Select all that apply. It refers to a fraction, ratio, or percent. It is not useful for summarizing nominal data. It can refer to either a sample or population.

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

Which of the following is not true? Using a higher confidence level results in a bigger sample size. Larger larger standard deviation results in bigger sample sizes. Larger population means results and bigger sample sizes. Using a small margin of error results in a bigger sample size.

Larger population means results and bigger sample sizes.

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. The population mean and distribution shape. The median of a sample from the population.

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