Question Type 2: Finding the confidence interval for a given set of data and distribution for unknown variance Exercises

A factory measures diameters of 30 rods, obtaining sample mean 10.2 cm and standard deviation 0.48 cm. Assuming normality with unknown variance, find a 95% confidence interval for the true mean diameter.

A reaction time experiment yields 25 measurements with sample mean 10.5 s and sample standard deviation 1.2 s. Assuming normality with unknown variance, find a 95% confidence interval for the mean reaction time.

A nutritionist records the weights (kg) of 20 patients. The sample mean is 65 and sample standard deviation is 8. Assuming weights are normally distributed with unknown variance, find the 95% confidence interval for the true mean weight.

A sample of 16 measurements yields mean 200 and standard deviation 25. Find the 90% confidence interval for the true mean, assuming normality with unknown variance.

A manufacturer tests 12 light bulbs. The lifetimes (in hours) have sample mean $\bar x=1200$ and sample standard deviation $s=100$. Assuming normality with unknown variance, find a 95% confidence interval for the true mean lifetime.

Seven observations of a chemical concentration (mg/L) are 100, 102, 98, 101, 99, 103, 97. Assuming normality with unknown variance, find a 95% confidence interval for the true mean concentration.

Six employees’ annual salaries (in thousands) are 45, 50, 55, 60, 65, 70. Assuming salaries are normally distributed with unknown variance, find a 95% confidence interval for the mean salary.

Five completion times (minutes) for a task are 45, 50, 55, 60, 65. Assuming times are normally distributed with unknown variance, find a 90% confidence interval for the mean completion time.

For a school, grades out of 8 are assumed normally distributed with unknown variance. A sample of 10 students yields grades 4.5, 2.6, 5.0, 7.6, 2.3, 2.3, 7.7, 5.3, 1.6, 4.6. Find a 90% confidence interval for the mean grade.

Nine customers’ daily coffee consumption (cups) is 2.1, 3.5, 2.8, 2.9, 3.0, 2.7, 3.2, 3.1, 2.6. Assuming normality with unknown variance, find a 95% confidence interval for the mean cups consumed.

Eight test scores are 78, 85, 80, 74, 90, 88, 76, 82. Assuming scores are normal with unknown variance, find a 99% confidence interval for the population mean.

Thirteen measurements of a machine’s positional error give a sample mean 0.15 mm and standard deviation 0.05 mm. Assuming normality with unknown variance, find a 99% confidence interval for the true mean error.