Confidence Intervals - Mixed

It was found that in a sample of 90 teenage boys, 70% of them have received speeding tickets.  What is the 90% confidence interval of the true proportion of teenage boys who have received speeding tickets? 

• (0.621, 0.779)

• (0.591, 0.812)

• (0.584, 0.830)

• (0.615, 0.805)

Tags

CCSS.HSS.IC.B.4

A researcher at a major hospital wishes to estimate the proportion of the adult population of the U.S. that has high blood pressure.  How large a sample is needed in order to be 90% confident that the sample proportion will not differ from the true proportion by more than 5%?

• 9
• 271
• 164
• 542

Tags

CCSS.HSS.IC.B.4

A survey of 800 shoppers found that 17% of them shop on impulse.  What is the 98% confidence interval for the true proportion of shoppers who shop on impulse? 

• 0.148 < p < 0.192

• 0.136 < p < 0.204

• 0.144 < p < 0.196

• 0.139 < p < 0.201

Tags

CCSS.HSS.IC.B.4

A random sample of 15 people were selected and had their heart rate measured. If we were to construct a confidence interval estimate of the population mean without knowing the population standard deviation, how many degrees of freedom would we need?

Suppose that a confidence interval for hours worked by students was computed to be (8.82, 10.78). Which of these is a valid interpretation of this confidence interval?

• There is a 95% probability that the mean number of hours worked by all students is between 8.82 and 10.78 hours.

• There is a 95% probability that a randomly selected student worked between 8.82 and 10.78 hours.

• We are 95% confident that the population mean number of hours worked by all students is between 8.82 and 10.78 hours.

• We are 95% confident that the mean number of hours worked by the students in our sample is between 8.82 and 10.78 hours.

Tags

CCSS.HSS.IC.B.4

Thirty randomly selected students took a local final exam. If the sample mean was 92 and the standard deviation was 9.4, construct a 99% confidence interval estimate of 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.B.4

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

• Sample mean
• t*
• Sample standard deviation
• Sample size

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 estimate of the population mean repair.

• (1070, 2530)

• (1273, 2326)

• (1799, 1801)

• (1776, 1823)

Tags

CCSS.HSS.IC.B.4

The lifetime of a certain type of battery is known to be normally distributed with a standard deviation of 20 hours. A sample of 50 batteries had a mean lifetime of 120.1 hours. It is desired to construct a 99% confidence interval for the mean lifetime of this type of battery.

What is the Confidence Interval to one decimal place?

• (114.5, 125.6)

• (112.81, 127.4)

• (112.82, 127.38)

• (114.56, 125.64)

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