In a random sample of 1200 potential buyers, 376 indicated that they would consider purchasing a...

In a random sample of 1200 potential buyers, 376 indicated that they would consider purchasing a hybrid vehicle. Estimate the proportion of people that would consider purchasing a hybrid vehicle at a 96% confidence level. Critical Value: Your answer should contain three decimal places Confidence Interval: ( , ) Keep your answers as decimals (not percentages) and round your answers to 3 decimal places.

Solutions

Expert Solution

Solution :

Given that,

n = 1200

x = 376

Point estimate = sample proportion = = x / n = 376/1200=0.313

1 - = 1-0.313=0.687

At 96% confidence level

= 1 - 96%

= 1 - 0.96 =0.04

/2 = 0.02

Z/2 = Z0.02= 2.054 ( Using z table )

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

= 2.054 ( $\sqrt$ ((0.313*687) /1200 )

= 0.027

A 95% confidence interval f is ,

- E < p < + E

0.313-0.027 < p < 0.313+0.027

0.289<p<0.340

(0.289 , 0.340)

orchestra answered 1 year ago

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