7-2 Quiz Statistics

In a study using 10 samples, and in which the population variance is unknown, the distribution that should be used to calculate confidence intervals is

• a standard normal distribution.

• a t distribution with 9 degrees of freedom.

• a t distribution with 11 degrees of freedom.

• a t distribution with 10 degrees of freedom.

When should the t-distribution be used to find a confidence interval for the mean?

• When t is known

• When σ is unknown

• When n ≤ 30

• When n > 30

Find tα/2 when n = 25 for the 95% confidence interval for the mean.

• 2.06

• 2.63

• 1.71

• 1.30

A sample of size n = 14 has a sample mean x̄ = 11.9 and sample standard deviation s = 2.1. Construct a 99% confidence interval for the population mean μ.

• 10.4 < μ < 13.4

• 10.2 < μ < 13.6

• 11.4 < μ < 12.4

• 10.7 < μ < 13.1

The prices (in dollars) for a graphing calculator are shown below for 8 online vendors.

Estimate the true mean price for this particular calculator with 95% confidence.

130 157 124 124

145 136 126 144

• 127.7 < μ < 143.8

• 120.9 < μ < 150.6

• 125.8 < μ < 145.8

• 132.2 < μ < 139.3

A food snack manufacturer samples 7 bags of pretzels off the assembly line and weighs their contents. If the sample mean is 15.2 oz. and the sample standard deviation is 0.70 oz., find the 95% confidence interval of the true mean.

• 14.6 < μ < 15.8

• 12.1 < μ < 18.3

• 14.9 < μ < 15.5

• 13.7 < μ < 16.7

5 squirrels were found to have an average weight of 8.9 ounces with a sample standard deviation is 0.9. Find the 95% confidence interval of the true mean weight.

• 7.8 < μ < 10.0

• 6.4 < μ < 11.4

• 8.5 < μ < 9.3

• 8.1 < μ < 9.7

Six measurements were made of the magnesium ion concentration (in parts per million, or ppm) in a city's municipal water supply, with the following results. It is reasonable to assume that the population is approximately normal.

175 177 175 180 138 138

Construct a 90% confidence interval for the mean magnesium ion concentration.

• 145.7 < μ < 182.0

• 161.2 < μ < 166.4

• 147.3 < μ < 180.4

• 161.0 < μ < 166.7

The winning team's score in 5 high school basketball games was recorded. If the sample mean is 62.3 points and the sample standard deviation is 11.0 points, find the 98% confidence interval of the true mean.

• 25.4 < μ < 99.2

• 50.8 < μ < 73.8

• 57.4 < μ < 67.2

• 43.9 < μ < 80.7

Find t(α/2) for n = 18 and a 99% confidence interval.

• 2.898

• 2.552

• 2.567

• 2.878