E370 Test 2

If an interval estimate is said to be constructed at the 90% confidence level, the significance level would be

.1

A nursery sells trees of different types and heights. These trees average 60 inches in height with a standard deviation of 16 inches. Suppose that 75 pine trees are sold for planting at City Hall. What is the standard deviation for the sample mean?

1.85

A simple random sample of 64 observations was taken from a large population. The sample mean and the standard deviation were determined to be 320 and 120 respectively. The estimated standard error of the mean is

15

The population standard deviation of a large population is measured 160. A sample of 16 is taken from the population. What is the variance of the sampling distribution of the mean for this sample?

1600

Random samples of size 81 are taken from an infinite population with the mean and standard deviation equal to 200 and 18, respectively. The distribution of the population is unknown. The mean of the sampling distribution of 𝑥¯x¯ is

200

In order to determine an interval for the mean of a population with unknown standard deviation, a sample of 61 items is selected. The mean of the sample is determined to be 23. The number of degrees of freedom for the critical t value is

60

Which of the following meets the requirements of a simple random sample?

A population contains 10 members under the age of 25 and 20 members over the age of 25. The sample will include six people chosen at random, without regard to age.

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 fights 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 the mean = 10 minutes and the standard error = 0.8 minutes

For a given confidence level and sample size, which of the following is true in the interval estimation of the population mean when σ is known?

If the population standard deviation is larger, the interval is wider.

After computing a confidence interval, the user believes the results are meaningless because the width of the interval is too large. Which one of the following is the best recommendation?

Increase the sample size

How does the variance of the sample mean compare to the variance of the population?

It is smaller and therefore suggests that averages have less variation than individual observations.

Whenever estimating the confidence interval for the population proportion, which of the following is required?

Sample size and populations proportion should be such that 𝑛𝑝≥5np≥5 and 𝑛(1−𝑝)≥5

Susan would like to conduct a survey of homeowners in the Meadowbrook neighborhood to get their opinions on proposed road modifications in the area. Which of the following would be a stratified sampling?

Susan ensures that her sample contains a number of two-story, split-level, and ranch homes in her sample that corresponds to the number of homes in the neighborhood.

It is known that the population is not normally distributed. Also, the population standard deviation is not known. A sample of 6 items is selected from this population to develop an interval estimate for the mean of the population (µ). Choose the correct alternative below.

The sample size must be increased for constructing the confidence interval.

Confidence intervals of the population mean may be created for the cases when the population standard deviation is known or unknown. How are these two cases treated differently?

Use the z distribution when σ is known; use the t distribution when σ is unknown.

Given that a 95% confidence interval for the population mean is (6.5, 12.5), we can state that

We expect that 95% of all possible sample means drawn from the population will produce confidence intervals that include the population's mean (which makes us 95% confident that interval (6.5, 12.5) contains the population mean)

At an academically challenging high school, the average GPA of a high school senior is known to be normally distributed with a variance of 0.25. A sample of 20 seniors is taken and their average GPA is found to be 2.71. Assume that 𝑧0.05=1.645z0.05=1.645 and 𝑧0.1=1.282z0.1=1.282. The 90% confidence interval for the population mean GPA is:

[2.5261, 2.8939]

A 95% confidence interval for the population mean is determined to be between 100 and 120. If the confidence level is reduced to 90%, the confidence interval for µ

becomes narrower

As the number of degrees of freedom for the t distribution increases, the difference between the t distribution and the standard normal distribution

becomes smaller

Deanna has been hired to visit the local shopping mall to conduct a survey about the upcoming political election. She needs to select respondents at the mall and ask them questions about their voting tendencies. Suppose that Deanna decides to randomly select four stores in the mall and then approach each shopper in these stores and ask them to participate in the survey. Which of the following sampling techniques best describes Deanna's method?

cluster sampling

In the point estimation,

data from the sample is used to estimate the population parameter

As the sample size increases, the margin of error

decreases

The value added and subtracted from a point estimate in order to develop an interval estimate of the population parameter is known as the

margin of error

In order to construct the interval estimate of the population mean when σ is known and the sample is very small, the population

must have a normal distribution

The battery life of the iPhone is normally distributed with the mean of 8.0 hours and the standard deviation 1.5 hours. A random sample of 15 iPhones is taken. The sampling distribution of the sample means for the battery life is

normal

A simple random sample of 64 observations was taken from a large population. The sample mean and the standard deviation were determined to be 320 and 120 respectively. The sampling distribution of 𝑥¯x¯ is

normal because the sample size is ≥30

The national average price for regular gasoline in February 2012 was reported to be $3.52 per gallon with the standard deviation of $0.08. A random sample of 13 gas stations was taken. The sampling distribution of the sample mean for the gasoline price

not possible to say because the sample size it too small

The sample standard deviation is the point estimator of the

population standard deviation

Sampling distribution of 𝑥¯x¯ is the

probability distribution of the sample mean

The Central Limit Theorem (CLT) states that the

sample means of large-sized samples will be normally distributed regardless of the shape of their population distributions

The standard deviation of the sampling distribution of 𝑥¯x¯ is called the

standard error of the mean

Sampling distributions describe the distribution of

statistics

Deanna has been hired to visit the local shopping mall to conduct a survey about the upcoming political election. She needs to select respondents at the mall and ask them questions about their voting tendencies. Deanna decides to position herself by the only entrance to the mall and select every 10th shopper entering the mall to participate. Which of the following sampling techniques best describes Deanna's method?

systematic sampling

When s is used to estimate σ, the margin of error is computed by using

t distribution

As the size of the sample increases,

the standard error of the mean becomes smaller

For the interval estimation of µ when σ is known and the sample is large, the proper distribution to use is

the standard normal distribution

The confidence intervals for the population proportion are generally based on

the z distribution

In computing the standard error of the mean, the finite population correction factor is used when

𝑛/𝑁>0.05

What is the relationship between the expected value of the sample mean and the expected value of the population?

𝜇𝑥¯=𝜇

What is the relationship between the standard deviation of the sample mean and the population standard deviation?

𝜎𝑥¯=𝜎/√n