Question

an automotive manufacturer wants to know the proportion of new car buyers who prefer foreign cars over domestic. step 1 of 2 : suppose a sample of 958 new car buyers is drawn. of those sampled, 383 preferred foreign over domestic cars. using the data, estimate the proportion of new car buyers who prefer foreign cars. enter your answer as a fraction or a decimal number rounded to three decimal places.

Answer 1

The proportion of new car buyers who prefer foreign cars at 99% confidence interval would be (0.38, 0.275).

Since we have given that

Sample size n = 958

x = 383

So,

$p = \frac{x}{n} = \frac{383}{958} = 0.399$

At 99% level of significance, z = 2.58

So, interval would be

$p = +/- z\sqrt{\frac{p(1-p)}{n} } \\\\= 0.399 +/- 2.58*\sqrt{\frac{0.399*(1-0.399)}{958} } \\\\= 0.399 +/- 0.0124\\\\= (0.399 - 0.0124, 0.399 + 0.0124)$

= (0.38, 0.275)

Hence the answer is, The proportion of new car buyers who prefer foreign cars at 99% confidence interval would be (0.38, 0.275).

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