Question

In: Statistics and Probability

In a sample of 600 potential car buyers, 376 indicated that they would consider purchasing a...

In a sample of 600 potential car buyers, 376 indicated that they would consider purchasing a hybrid gas/electric-powered car. Find and interpret the 95% confidence interval (z*=1.96) for the true population proportion of potential car buys that would consider purchasing a hybrid vehicle. Round your answer to 3 decimal places.

Expert Solution

Solution :

Given that,

n = 600

x = 376

Point estimate = sample proportion = = x / n = 376/600=0.627

1 - = 1- 0.627 =0.373

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 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 ( $\sqrt$ ((0.627*0.373) / 600)

E = 0.039

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.627-0.039 < p <0.627+ 0.039

0.588< p < 0.666

The 95% confidence interval for the population proportion p is : 0.588, 0.666

orchestra answered 2 years ago

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