Eric is studying people's typing habits. He surveyed 525 people and asked whether they leave one space or two spaces after a per

Question

2 months ago

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Eric is studying people's typing habits. He surveyed 525 people and asked whether they leave one space or two spaces after a per

iod when typing. 440 people responded that they leave one space. Create a 90% confidence interval for the proportion of people who leave one space after a period. Round your results to four decimal places.

Mathematics

1 answer:

lawyer [12.5K] · Answer 1 · 2026-03-23T02:40:39+03:00

Response: (0.8115, 0.8645)

Step-by-step outline:

Define p as the proportion of individuals who leave one space after a sentence.

Provided: Sample size: n= 525

Number of respondents indicating they leave one space: 440

Thus, the sample proportion is: $\hat{p}=\dfrac{440}{525}\approx0.838$

The z-score for a 90% confidence interval is: 1.645

The formula for determining the confidence interval:

$\hat{p}\pm z^*\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$

$0.838\pm (1.645)\sqrt{\dfrac{0.838(1-0.838)}{525}}\\\\=0.838\pm (1.645)\sqrt{0.00025858285}\\\\=0.838\pm (1.645)(0.01608)\\\\= 0.838\pm0.0265\\\\=(0.838-0.0265,\ 0.838+0.0265)\\\\=(0.8115,\ 0.8645)$

Consequently, a 90% confidence interval for the proportion of people who leave one space after a period is: (0.8115, 0.8645)