Confidence Intervals

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Suppose we flip a coin 100 times and count 60 heads. Let p be the (unknown) probability that the coin comes up heads on a flip. Give an approximate 95% confidence interval for the value of p.

Suppose in a sample of 100 people, 12 are left-handed.

Give a 95% confidence interval for the proportion p of left-handed people.

Give a 90% confidence interval.

The weights of five mice are measured and recorded below. Give a 95% confidence interval for the sample mean weight of mice. (Pretend 5 measurements is large enough for the CLT to apply.)

mouse i 1 2 3 4 5 weight \widetilde{w}_i (g) 26 32 33 20 29

The heights of five plants are measured and recorded below. Give a 95% confidence interval around the sample mean for the heights of the plants. (Pretend 5 measurements is large enough for the CLT to apply.)

plant i 1 2 3 4 5 height \widetilde{h}_i (in) 15 14 18 21 17