AP Stat Confidence Intervals

A sample size of n = 64 is drawn from a population whose standard deviation is σ = 5.6.

Find the margin of error for a 99% confidence interval for µ.

A large sample has mean of 7.1 and Standard Error of 2.3.

Construct a 90% Confidence Interval for the population mean µ (to two decimal places).

An IQ test was given to a simple random sample of 75 students at a certain college. The sample mean score was 105.2. Scores on this test are known to have a standard deviation of 10. It is desired to construct a 90% confidence interval for the mean IQ scores of the students at the college. What is the point estimate?

An IQ test was given to a simple random sample of 75 students at a certain college. The sample mean score was 105.2. Scores on this test are known to have a standard deviation of 10. It is desired to construct a 90% confidence interval for the mean IQ scores of the students at the college. Find the Margin of Error to two decimal places.

Hint: think logically...

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?

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

How do you reduce the margin of error?

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. What is the population proportion that has diabetes according to this confidence interval? ​ What was the margin of error associated with this data? ​

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?