A researcher is interested in the average time served in jail for robbery. They take a sample of 400 convictions, and find the average time served is

A confectionery company manufactures a popular brand of chocolate chip cookies that claims to have at least 15 chocolate chips in each cookie. A student is doubtful and wanted to estimate the number of chocolate chips in this brand of cookie. They sampled 100 cookies of this popular brand and found an average of 12.5 chips per cookie. If we assume the machine in the confectionery company that makes the cookies has a mean \mu and standard deviation \sigma = 8 chocolate chips per cookie, a 99% confidence interval for the average number of chips per cookie based on this sample was found to be (10.4, 14.9). Is the student’s doubt about the company’s claim reasonable?

You plan to construct a 99% confidence interval for the mean of a Normal population with (known) standard deviation . By using a sample size of 400 rather than 100, you can reduce the margin of error by a factor of

The amount of time customers at a “Quick-Change” motor oil store spend waiting for their cars to be serviced has the Normal distribution with mean μ and standard deviation σ = 4 minutes. It is company policy that the customer wait time should be 20 minutes (or less). The manager of a particular store selects a random sample of 150 customer wait times and observes a mean wait time of 21 minutes.

I computed a 95% confidence interval for the mean lifetime of a set of tires as (37,000, 42,000) kilometres. Based on this interval, I know:

The population of the scores of all high school seniors that took the ATAR-M test (mathematics component of the ATAR test) last year followed a Normal distribution, with mean \mu and standard deviation \sigma= 100. You read a report that says, “On the basis of a simple random sample of 500 high school seniors that took the ATAR-M test this year, a confidence interval for is 512.00 ± 11.52.”

A bottling plant produces one-litre bottles of soda. The actual distribution of volumes of soda dispensed to bottles is Normal, with mean μ and standard deviation σ = 0.05 litre. We randomly select eight (8) bottles and measure the volume of soda in each. The results of these eight measurements (all in litre units) are

If they want to calculate a 95% confidence interval for μ, they should

A student wanted to estimate the number of chocolate chips in a commercial brand of cookie. They sampled 100 cookies and found an average of 10.5 chips per cookie. If we assume the standard deviation is 8, what is a 99% confidence interval for the average number of chips per cookie?

Twenty-five seniors from a large metropolitan area school district volunteer to allow their maths ATAR test scores to be used in a study. These 25 seniors had a mean maths ATAR score of 450. Suppose we know that the standard deviation of the population of maths ATAR scores for seniors in the district is \sigma = 100. Assuming the population of maths ATAR scores for seniors in the district is approximately Normally distributed, a 90% confidence interval for the mean maths ATAR score \mu for the population of seniors computed from these data is

A bottling plant produces one-litre bottles of soda. The actual distribution of volumes of soda dispensed to bottles is Normal, with mean μ = 0.956 litre and standard deviation σ = 0.05 litre. We randomly select six (6) bottles and measure the volume of soda in each. The results of these six measurements (all in litre units) are

Which of the following statements are true about constructing 90% confidence intervals from samples such as this one?

Select all correct answers: