Matched Pairs Confidence Intervals

A school administrator is interested in estimating the proportion of students in the district who participate in community service activities. From a random sample of 100 students in the district, the administrator will construct a 99 percent confidence interval for the proportion of all district students who participate in community service activities. Which of the following statements must be true?

• The population proportion will be in the confidence interval.

• The probability that the confidence interval will include the population proportion is 0.99.

• The probability that the confidence interval will include the sample proportion is 0.99.

• The population proportion and the sample proportion will be equal

• The probability that the population proportion and the sample proportion will be equal is 0.99.

The lifetime of a certain type of batter 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)

• (112.8, 127.4)

• (112.82, 127.38)

• (114.56, 125.64)

If the 95% Confidence Interval for a population mean is (114.56, 125.54), then is it likely that the true population mean µ is greater than 130?

• Yes

• No

• Not enough information

• I have no idea what you're asking of me

75 randomly selected people were asked to run a lap around the track on Monday with Nike sneakers on and have their time recorded. The same 75 people were asked to run a lap around the track on Tuesday with Adidas sneakers on and have their time recorded. Which would be the appropriate significance test to determine whether or not people Nike sneakers are faster than Adidas sneakers?

• 2-Proportion Z-test

• 2-mean T-Test

• Matched Pairs T-Test

• 1 mean T-Test

Percentiles of the bootstrap distribution are provided. Use the percentiles to report a 95% confidence interval for the parameter.

• 6.593 hours to 7.78 hours

• 6.322 hours to 8.082 hours

• 6.438 hours to 7.947 hours

• 6.174 hours to 8.304 hours

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.

A 95% confidence interval was conducted on American adults aged 45-64 and found that the between 15.7% and 19.4% had diabetes as of 2016.

a) What is the population proportion that has diabetes according to this confidence interval? ​ (a)  

b) What was the margin of error associated with this data? ​ (b)  

• 17.55%

• 1.85%

• 11.55

• 5.775

• 11.55%

• 5.775%

47 students from Lyndhurst HS and 62 students from Rutherford HS were asked how many times a year they go to American Dream mall. The mean and standard deviation for Lyndhurst was 9.27 and 4.8, while the mean and standard deviation for Rutherford was 12.55 and 6.2. Does this provide convincing evidence at the .01 level that Rutherford HS students go to American Dream mall at least 2 more times a year than Lyndhurst HS students? Show ALL of your work in the box and give the FULL explanation!

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

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