Confidence intervals worksheet with answers

A laboratory measures a quantity 25 times; the measurement standard deviation is known to be 13.5. How wide W is the 95% confidence interval for the true mean (upper limit minus lower limit)?

A laboratory measures a quantity 50 times; the measurement standard deviation is known to be 12. How wide W is the 99% confidence interval for the true mean (upper limit minus lower limit)?

The battery life of two phone models is compared. Model 1: 60 phones, mean 93.5 h, known standard deviation 10 h. Model 2: 30 phones, mean 90 h, known standard deviation 13 h. Find the upper limit of the 95% confidence interval for μ₁ − μ₂.

The blood pressure of 8 patients is measured before and after a treatment. The differences d = before − after (mmHg) have mean 7.8 and standard deviation 3.5. Find the margin of error E of the 90% confidence interval for the mean difference.

The population standard deviation is 22. How large a sample n do you need so that a 95% confidence interval for the mean has a margin of error of at most 1?

The diameters of 11 machined shafts have a sample standard deviation of 7.2 µm. Assuming the diameters are normally distributed, find the lower limit σ of the 95% confidence interval for the population standard deviation. With df = 10, 2.5% of the χ² distribution lies below 3.247 and 2.5% lies above 20.483.