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## Section 4.3 Confidence Intervals

Text of section.
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### Exercises Exercises

#### 1.

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 \(p\text{.}\)
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#### 2.

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

Give a 95% confidence interval for the proportion \(p\) of left-handed people.
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##### (b)

Give a 90% confidence interval.
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#### 3.

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.)
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Table 4.3.1.
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mouse \(i\) | 1 | 2 | 3 | 4 | 5
--- | --- | --- | --- | --- | ---
weight \(\widetilde{w}_i\) (g) | 26 | 32 | 33 | 20 | 29

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#### 4.

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.)
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Table 4.3.2.
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plant \(i\) | 1 | 2 | 3 | 4 | 5
--- | --- | --- | --- | --- | ---
height \(\widetilde{h}_i\) (in) | 15 | 14 | 18 | 21 | 17

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