Confidence Intervals and Sample Size

Find the critical value, z* for 97%

• 1.88

• 2.17

• -1.88

• -2.17

Which confidence would result in a wider interval (assuming nothing else changed), 91% or 97%?

• 97%, z* is larger for higher confidence intervals

• 97%, the standard error is larger for higher confidence intervals

• 91%, z* is larger for lower confidence intervals

• 91%, the standard error is smaller for lower confidence intervals

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.

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, 0.780)

• (0.591, 0.812)

• (0.584, 0.830)

• (0.615, 0.805)

This is notation from a different book. Identify the confidence interval used in the figure below if each shaded area is equal to 0.05.

• 90%

• 95%

• 98%

• 99%

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

A recent study of 750 Internet users in Europe found that 35% of Internet users were women.  What is the 95% confidence interval of the true proportion of women in Europe who use the Internet? 

• 0.321 < p < 0.379

• 0.316 < p < 0.384

• 0.309 < p < 0.391

• 0.305 < p < 0.395

Which of the following actions would produce a confidence interval with a smaller width assuming all other contingencies remained constant?

• Using a higher confidence level

• Using a lower confidence level

A sample of 20 cupcakes found the interval for average calories to be (150, 350). Which is the correct interpretation of the 95% confidence interval?

• We are 95% confident that the true mean caloric content can be found with a sample of 150 to 350 cupcakes.

• We are 95% confident that the interval (150, 350) captures the true average caloric content.

• We are 95% confident that a sample of 20 cupcakes will find 250 calories per cupcake.

• None of these are correct.

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