Confidence intervals worksheet with answers

In a poll of 1000 randomly chosen voters, 750 support a proposal. Find the upper limit of the 95% confidence interval for the proportion of supporters.

A 90% confidence interval for a mean, computed from 64 observations with a known population standard deviation, is [130.15, 140.85]. What standard deviation σ was used?

The battery life of two phone models is compared. Model 1: 100 phones, mean 84.5 h, known standard deviation 20 h. Model 2: 80 phones, mean 86 h, known standard deviation 14 h. Find the margin of error E of the 99% confidence interval for μ₁ − μ₂.

A sample of 30 items has mean 11 and standard deviation s = 2.5. The population is roughly normal. Find the upper limit of the 90% confidence interval for the mean.

Two fertilisers are tested. Plot group 1: 5 plots, mean yield 28.5 kg, standard deviation 3 kg. Plot group 2: 7 plots, mean 19.5 kg, standard deviation 4 kg. Assume equal variances (pooled t, df = n₁ + n₂ − 2). Find the margin of error E of the 95% confidence interval for μ₁ − μ₂.

The diameters of 10 machined shafts have a sample standard deviation of 5.2 µm. Assuming the diameters are normally distributed, find the upper limit σ of the 95% confidence interval for the population standard deviation. With df = 9, 2.5% of the χ² distribution lies below 2.7 and 2.5% lies above 19.023.