A survey of 547 Americans was asked if commuting to work was stressful. 24% of them...

A survey of 547 Americans was asked if commuting to work was stressful. 24% of them said that it was. Find a 95% confidence interval for the proportion of American that find commuting to work stressful.

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Expert Solution

Solution :

Given that,

n = 547

Point estimate = sample proportion = = 0.24

1 - = 1-0.24=0.76

At 95% confidence level

= 1 - 95%

= 1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z0.025 = 1.96 ( Using z table )

Margin of error = E = Z / 2 * $\sqrt$ (( * (1 - )) / n)

= 1.96 ( $\sqrt$ ((0.24*0.76) / 547)

= 0.036

A 95% confidence interval for proportion p is ,

- E < p < + E

0.24-0.036 < p <0.24+0.036

0.204<P<0.276

orchestra answered 1 year ago

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