In 1980 more than 35% of cars purchased had a manual transmission (i. e. stick shift). By 2007 the proportion had decreased to 7.7%. A random sample of college students who owned cars revealed the following: out of 133 cars, 31 had stick shifts. Estimate the proportion of college students who drive sticks with 90% confidence. Use a graphing calculator and round the answers to at least three decimal places. <

The 90% confidence interval for the proportion of college students who drive sticks is (0.173, 0.293).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of , we have the following confidence interval of proportions.

In which

z is the zscore that has a pvalue of .

A random sample of college students who owned cars revealed the following: out of 133 cars, 31 had stick shifts.

This means that

90% confidence level

So , z is the value of Z that has a pvalue of , so .

The lower limit of this interval is:

The upper limit of this interval is:

The 90% confidence interval for the proportion of college students who drive sticks is (0.173, 0.293).

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