AP Statistics Confidence Intervals

In a survey of 104 students, it was found that 79 went to the homecoming game this year.

Calculate a 99% confidence interval for p.

• (0.652, 0.868)

• (0.691, 0.829)

• (0.678, 0.842(

• (0.685, 0.895)

In a survey of 104 students, it was found that 79 went to the homecoming game this year. A 99% confidence interval for p is (0.652, 0.868). Interpret this interval.

• 99% of the time the true proportion of people who went to the homecoming game this year is between 65.2% and 86.6%.

• The probability that the population proportion of people who went to the homecoming game this year is between 65.2% and 86.6% is 95%.

• Based on this sample, I am 99% confident that the true proportion of people who went to the homecoming game this year is between 65.2% and 86.6%.

• 99% of all possible intervals calculated this way will capture the true proportion of people who went to the homecoming game this year

A preliminary study suggests that 87% of people agree on an issue. How large must your sample size be so you could be within ± 3% of p calculate at 90% confidence?

• 7

• 466

• 5

• 338

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

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%

A recent survey of 2000 high schoolers found that 80% use their phones more than 4 hours a day on average. What is the interval for which we could expect to find the truth of the population?

• 2%

• 78% - 82%

• 93% - 97%

• 82%

• A
• B
• C
• D

The manufacturer of a smart watch claims that individuals who pay attention to how many steps they take per day will inadvertently take more steps per day than individuals who pay no attention to how many steps they take per day. To investigate this claim, the manufacturer conducts a study to estimate the difference in the mean number of steps taken by those that pay attention to how many steps they take per day and those that do not. To do so, 40 volunteers are recruited. Half of the volunteers are randomly assigned to receive a smart watch and are taught how to use it to track their steps. The other half of the volunteers are given a wristband to wear, but are not informed that the wristband is tracking their steps. The volunteers are monitored for 30 days. The mean and standard deviation of the number of steps taken per day are computed for each group. The data are shown above. Which of the following is a 99% confidence interval for the difference in the mean number of steps taken by all people like these that do and do not pay attention to the number of steps they take per day using df = 19?

• 
• 
• 
• 
• 

Identify the confidence interval used in the figure below if each shaded area is equal to 0.05.

• 90%

• 95%

• 98%

• 99%

The National Honor Society at Central High School plans to sample a random group of 100 seniors from all high schools in the state to determine the average number of hours per week spent on homework. A 95 percent confidence interval for the mean number of hours spent on homework will then be constructed using the sample data. Before selecting the sample, the National Honor Society decides that it wants to decrease the margin of error. Which of the following is the best way to decrease the margin of error?

• Increase the confidence level to 99%

• Use the population standard deviation

• Use the sample standard deviation

• Decrease the sample size

• Increase the sample size