Confidence Interval Standard Deviation and Variance

Confidence intervals allow us to....

• Find a range for the sample mean using the population standard deviation.

• Find the population mean to four decimal places.

• Find a range for the population mean using a sample mean.

• Find the probability that the population mean is the same as the sample mean.

When calculating Confidence Intervals, if we don't know the population standard deviation, we need to:

• Make it up.

• Estimate sigma with s, and use the z distribution.

• Give up.

• Estimate sigma with s, and use the t distribution.

When calculating Confidence Intervals, if we know the population standard deviation, but the population is NOT normally distributed, we...

• Use z if the sample size is at least 30

• Always use t.

• Always use z.

• Use z if the sample size is less than 30.

A sample of 20 cakes found the 95% confidence interval for average calories (per cake) to be (150, 350). Which is the correct interpretation (explanation) of this interval?

• We are 95% confident that the population mean can be found with a sample of 150 to 350 cakes.

• We are 95% confident that the interval (150, 350) contains the population mean (calories per cake).

• We are 95% confident that a sample of 20 cakes will have a sample mean of 250 calories per cake.

• None of these are correct.

The sample mean is always...

• The same as the population mean.

• In the middle of the confidence interval.

• Outside of the confidence interval.

• Smaller than the population mean.

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 batch are normally distributed.

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

• The standard deviation for the population is unknown.