Chapter 8-9

The general formula for a confidence interval is:

-a point estimate is the sample measurement in question (mean, proportion) -the margin of error is made up of a critical value multiplied by the standard error

Confidence intervals

-characterized by a confidence level -the confidence level is a probability and is usually designated by a % - it tells us Exactly how sure we are about the accuracy of our interval

A random sample of 100 boxes of cereal had a sample mean weight of 396 grams. The standard deviation is known to be 5 grams. The upper end of the confidence interval for the mean is 405.8 grams.

False

Hypothesis testing and confidence interval estimation are essentially two totally different statistical procedures and share little in common with each other.

False

To construct a 99 percent confidence interval where σ is known, the correct critical value is 1.96.

False

Estimating the population proportion p

Keep in mind that p can never be less than 0 or greater than 1, so the upper limit is bounded by 1 and the lower limit is bounded by 0

If we are performing a two-tailed test of whether μ = 100, the probability of detecting a shift of the mean to 105 will be ________ the probability of detecting a shift of the mean to 110.

Less Than

A report in a consumer magazine indicated that with 90 percent confidence, the mean number of hours that a particular brand light bulb lasts is between 900 and 1,100 hours. Based on this, the sample mean that produced this estimate is 1,000 hours.

True

A two-tailed hypothesis test with α = 0.05 is similar to a 95 percent confidence interval.

True

In a situation where we know the population standard deviation but wish to estimate the population mean using a 90 percent confidence interval, the critical value is z = ±1.645.

True

In hypothesis testing, the null hypothesis should contain the equality sign.

True

Sampling error is the difference between a statistic computed from a sample and the corresponding parameter computed from the population.

True

The significance level in a hypothesis test corresponds to the maximum probability that a Type I error will be committed.

True

The chamber of commerce in a beach resort town wants to estimate the proportion of visitors who are repeat visitors. Suppose that they have estimated that they need a sample size of n=16,577 people to achieve a margin of error of ± .01 percentage points with 99 percent confidence, but this is too large a sample size to be practical. How can they reduce the sample size?

Use a lower level of confidence

A statement in the newspaper attributed to the leader of a local union stated that the average hourly wage for union members in the region is $13.35. He indicated that this number came from a survey of union members. If an estimate was developed with 95 percent confidence, we can safely conclude that this value is within 95 percent of the true population mean hourly wage.

false

Which of the following will result in a larger margin of error in an application involving the estimation of a population mean

increasing the sample standard deviation

Mike runs for the president of the student government and is interested to know whether the proportion of the student body in favor of him is significantly more than 50 percent. A random sample of 100 students was taken. Fifty-five of them favored Mike. At a 0.05 level of significance, it can be concluded that the proportion of the students in favor of Mike

is not significantly greater than 50 percent

The power of a test is measured by its capability of:

rejecting a null hypothesis that is false

When σ is unknown, the margin of error is computed by using:

t-distribution

A hypothesis test is to be conducted using an alpha = .05 level. This means:

there is a maximum 5 percent chance that a true null hypothesis will be rejected.

The purpose of a pilot sample is:

to provide an idea of what the population standard deviation might be