Chapter 7 In Class Match Up +2

Boxes of cereal are labeled as containing 14 ounces. Following are the weights, in ounces, of a sample of 16 boxes. It is reasonable to assume that the population is approximately normal.

Construct a 99.5% confidence interval for the mean weight.

• 14.046 to 14.167

• 14.057 to 14.345

• 15.046 to 16.167

• 14.446 to 14.867

The margin of error is the product of the standard error and the

• confidence level
• critical value

• mean
• population size

When constructing a confidence interval for a population mean μ from a sample of size 19, the number of degrees of freedom for the critical value is

• 21
• 20
• 18
• 17

Emily and Julio are going to construct confidence intervals from different simple random samples. Both confidence intervals will have level 90%. Emily will use a sample of size 60, and Julio will use a sample of size 90. The samples will be drawn from the same population.

Which confidence interval will have the larger margin of error? Or will they both be the same?

• Cannot be determined
• They will be the same
• Emily's
• Julio's

Answer explanation

If we increase sample size, we get more information, a lower margin of error, and a narrower interval. If we decrease sample size, we get less information, a higher margin of error, and a wider interval.

Since Emily's sample size,60, is lower than Julio's sample size,90, the interval Emily constructs will have the larger margin of error.

Emily and Julio are going to construct confidence intervals from different simple random samples. Both confidence intervals will have level 90%. Emily will use a sample of size 60, and Julio will use a sample of size 90. The samples will be drawn from the same population.

Which confidence interval is more likely to cover the population mean? Or are they both equally likely to do so?

• Cannot be determined
• They are both equally likely to do so

• Emily's
• Julio's

Answer explanation

The confidence level is equal to the percent of such confidence intervals that cover the population mean.

Since both Emily and Julio are using the same confidence level, their confidence intervals are equally likely to cover the population mean.

A simple random sample of

27 colleges and universities in the United States had a mean tuition of $18,295 with a standard deviation of $9726.

What method is appropriate here to construct a confidence interval for the mean?

• z-distribution method, because we have the population standard deviation.

• t-distribution method, because we have the sample standard deviation.

• Neither method is appropriate, since the sample size is too small and we do not know if the population is approximately normal.

A college admissions officer sampled 122 entering freshmen and found that 42 of them scored more than 550 on the math SAT.

Find a point estimate for the proportion of all entering freshmen at this college who scored more than 550 on the math SAT.

• 0.2754
• 0.4213
• 0.5126
• 0.3443

A college admissions officer sampled 122 entering freshmen and found that 42 of them scored more than 550 on the math SAT.

Construct an 80% confidence interval for the proportion of all entering freshmen at this college who scored more than 550 on the math SAT.

• 0.100 to 0.200
• 0.289 to 0.399

• 0.700 to 0.800
• 0.280 to 0.408

A sample of size 35 has sample mean 54 and sample standard deviation 6.8.

Construct a 90% confidence interval for the population mean μ.

• 52.1 to 55.9

• 53.2 to 57.8

• 53.4 to 60

• 45.6 to 55

A sample of size 35 has sample mean 54 and sample standard deviation 6.8.

If the sample size were 44, would the confidence interval be narrower or wider?

• wider
• same
• narrower
• not enough information