Question

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

Answer 1

Answer: (0.8115, 0.8645)

Step-by-step explanation:

Let p be the proportion of people who leave one space after a period.

Given:  Sample size : n= 525

Number of people responded that they leave one space. =440

i.e. sample proportion: $\hat{p}=\dfrac{440}{525}\approx0.838$

z-score for 90% confidence level : 1.645

Formula to find the confidence interval :

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

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

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