Confidence Intervals Basics

A sample of 40 people owned an average of 1.35 apple products. It is known from a previous study that the population standard deviation of apple product ownership is 0.63 products. Construct a 95% confidence interval.

• (1.11, 1.58)
• (1.15, 1.55)
• (1.19, 1.51)
• (1.09, 1.61)

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.4

CCSS.HSS.ID.A.4

A random sample of 150 students has a grade point average with a mean of 2.86.  Assume the population standard deviation is 0.78.  Construct the confidence interval for the population mean if c = 0.98.

• (2.51, 3.53)
• (2.43, 3.79)
• (2.31, 3.88)
• 2.71, 3.01)

In a survey of 2480 golfers, 15% said they were left-handed.  The survey's margin of error was 3%.  Construct a confidence interval for the proportion of left-handed golfers.

• (0.18, 0.21)
• (0.12, 0.18)
• (0.12, 0.15)
• (0.11, ).19)

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.4

When interpreting the confidence interval, make sure that you are describing the

• statistic

• parameter

The 99% confidence interval for a proportion is (0.54, 0.72). What is p̂?

• 0.63

• 0.18

• 0.09

• 0.66

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.4

Agricultural researchers plant 100 plots with a new variety of corn and measure the mean yield for these plots in bushels per acre. They treat the 100 plots as a simple random sample of possible plots of corn (as researchers often do) and report a 95% confidence interval for the mean corn yield of (128.4, 131.6) bushels per acre. Which of the following is a correct interpretation of the 95% confidence level (notice it's asking for level not interval!)?

• We are 95% confident that the true mean yield for this new variety of corn is captured by the interval (128.4, 131.6) bushels per acre
• If many intervals were constructed this way from many independent sets of 100 plots, 95% of the intervals would capture the true mean corn yield.
• If many intervals were constructed this way from many independent sets of 100 plots, 95% of the time the true mean corn yield would be in the interval (128.4, 131.6) bushels per acre.

Tags

CCSS.HSS.IC.B.4

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