Question

Manual Transmission Automobiles In a recent year,

6%

of cars sold had a manual transmission. A random sample of college students who owned cars revealed the following: out of

126

cars,

28

had manual transmissions. Estimate the proportion of college students who drive cars with manual transmissions with

90%

confidence. Round intermediate and final answers to at least three decimal places.

Answer 1

We need to construct the 90% confidence interval for the population proportion. We have been provided with the following information about the number of favorable cases:

Favorable Cases X =	28
Sample Size N=	126

The sample proportion is computed as follows, based on the sample size N=126 and the number of favorable cases X = 28

The critical value for α=0.1 is The corresponding confidence interval is computed as shown below:

Therefore, based on the data provided, the 90\%90% confidence interval for the population proportion is 0.161<p<0.283, which indicates that we are 90\%90% confident that the true population proportion pp is contained by the interval (0.161, 0.283).

porportion of college students who drive cars with manual transmission lies between 0.161<p<0.283

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