Confidence Intervals for the Mean (both large and small samples)

A sample of 30 women finds the mean height to be 62.3 in and the standard deviation to be 1.5 in. Find the margin of error of women's heights with a 95% CL.

• 1.699
• 0.56
• 0.537
• 19.325

Find the t* value for a 99% confidence interval with a sample of 23 people.

• 1.714
• 1.711
• 2.064
• None of these.

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. 

• (1070, 2530)
• (1273, 2326)
• (1799, 1801)
• None of these.

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.

• 89.08 < μ < 94.92 
• 87.27 < μ < 96.73
• 87.29 < μ < 96.71 
• 87.77 < μ < 96.23

A 90% confidence interval for the average salary of all CEOs in the electronics industry was constructed using the results of a random survey of 45 CEOs. The interval was ($139,048, $154,144). Give a practical interpretation of the interval.

• 90% of the sampled CEOs have salaries that fell in the interval $139,048 to $154,144
• We are 90% confident that the mean salary of all CEOs in the electronics industry falls in the interval $139,048 to $154,144. 
• 90% of all CEOs in the electronics industry have salaries that fall between $139,048 to $154,144
• We are 90% confident that the mean salary of the sampled CEOs falls in the interval $139,048 to $154,144.

A researcher studying reaction time of drivers states that, “A 95% confidence interval for the mean time it takes for a driver to apply the brakes after seeing the brake lights on a vehicle in front of him is 1.2 to 1.8 seconds.  What are the point estimate and margin of error for this interval?

• Point estimate = 1.2 seconds; margin of error = 0.6 seconds.
• Point estimate = 1.2 seconds; margin of error = 0.3 seconds.
• Point estimate = 1.5 seconds; margin of error = 0.6 seconds.
• Point estimate = 1.5 seconds; margin of error = 0.3 seconds.

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

Construct a 95% confidence interval for the population mean, mu.  Assume the population has a normal distribution.  A sample of 25 randomly selected students has a mean test score of 81.5 with a standard deviation of 10.2

• (77.29, 85.71)
• (87.12, 98.32)
• (66.35, 69.89)
• (56.12, 78.34)