6.1-6.2

Identify the confidence interval used in the figure below if each shaded area is equal to 0.05.

• 90%
• 95%
• 98%
• 99%

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.4

CCSS.HSS.ID.A.4

The confidence level of an interval estimate of a parameter is the probability that the interval estimate will contain the parameter.

• True
• False

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.4

CCSS.HSS.ID.A.4

Thirty randomly selected students took the calculus final. If the sample mean was 92 and the standard deviation was 9.4, construct a 99 percent confidence interval for the mean score of all students from which the sample was gathered.

• 89.08 < μ < 94.92

• 87.27 < μ < 96.73

• 87.29 < μ < 96.71

• 87.77 < μ < 96.23

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.4

CCSS.HSS.ID.A.4

Which of the following changes to a study would result in a narrower confidence interval?

• increasing the confidence level, increasing the sample size
• decreasing the confidence level, decreasing the sample size
• increasing the confidence level, decreasing the sample size
• decreasing the confidence level, increasing the sample size.

Tags

CCSS.HSS.IC.B.4

In a crash test of 15 troopers, collision repair costs are found to have a distribution that is approximately normal, with a mean of $1800 and a standard deviation of $950. Construct a 99% confidence interval for the repair cost for the population.

• (1070, 2530)

• (1273, 2326)

• (1799, 1801)

• (1776, 1823)

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.4

CCSS.HSS.ID.A.4

Which of the following does NOT have an affect on the width of a confidence interval?

• Sample mean

• $t_c$

• Sample standard deviation

• Sample size

A research group wishes to estimate the mean amount of time (in hours) that members of a fitness center spend exercising each week. They want to estimate the mean within a margin of error of 0.5 hours with a 95% level of confidence. Previous data suggests that the standard deviation of the population is 2.2. Which of the following is the smallest sample size they could use?

• 60

• 75

• 90

• 180

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.4

Given the same mean, SD, and sample size, a confidence interval of 80% would be wider than a confidence interval of 90%

• True
• False

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.4

Determine the minimum sample size needed to construct a 95% confidence interval for the mean age of employees at a company. The estimate must be accurate to within 0.5 year. Assume the standard deviation is 4.8 years.

• 18

• 19

• 354

• 355

Find the critical value tc necessary to form a 95% confidence interval with a sample size of 15.

• 2.131

• 1.960

• 2.145

• 2.120