Difference in Means Confidence Intervals

Daniel and Tyron want to estimate the same population mean. Daniel collects a sample of 100 observations, Tyron of 200 observations. They both calculate 95% CI's.

• Daniels CI is roughly 2 times larger than Tyrons

• Daniels CI is roughly 1.5 times larger than Tyrons

• Daniels and Tyrons CI are roughly of the same size

• Daniels CI is two times smaller than Tyrons

The economist published a new (hypothetical) poll for the US presidential election: The 95% CI's for the voting share equal: Biden 44% +/- 1% and Trump 43% +/- 1%. What can we conclude?

• Biden is clearly leading

• There is no significant difference between both

• Trump is clearly leading

• A third party candidate is clearly leading

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.

120 Brand X oil filters and 90 Brand Y oil filters were tested for milligrams of residue, with the following results. Find a 95% confidence interval for μY - μX.

• (0.96, 1.44)

• (0.92, -0.96)

• (-1.44, -0.96)

• (-1.84, -0.56)

• (0.92, 1.48)

A 90% confidence interval for the mean speed driven by cars on Due West Road is given by (21, 45). What was the sample mean of this study?

• 12

• 24

• 33

• None of these.

A quality control inspector will measure the salt content (in milligrams) in a random sample of bags of potato chips from an hour of production. Which of the following would result in the smallest margin of error in estimating the mean salt content μ?

• 90% confidence; n = 25

• 90% confidence; n = 50

• 95% confidence; n = 25

• 95% confidence; n = 50

• n=100 at any confidence level

A sample of 121 high school seniors were surveyed on their level of school spirit on a scale of 0-100. The sample mean of this survey is 86. The known population standard deviation is 14 for all seniors in the class. Which of these is a 95% confidence interval for the population mean?

• [82.7, 89.3]

• [83.5, 88.5]

• [83.9, 88.1]

• [85.9, 86.1]

A quality control specialist at a glass factory must estimate the mean clarity rating for a new batch of glass using a sample of 18 glass sheets from the batch. Past investigations show that clarity ratings are normally distributed. The specialist decides to use a t-distribution rather than a z-distribution because ...

• The t distribution is more accurate than a z distribution.

• Clarity ratings for the entire bacth are normally distributed.

• The t-distribution will create a narrower interval than z.

• The standard deviation for the population is unknown.

A 90% confidence interval for the mean speed driven by cars on Due West Road is given by (21, 45). What was the margin of error of this interval?

• 12

• 24

• 33

• None of these.

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 to $154,144. Give the 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.

• There is a 90% chance that 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.