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Proportion of Adults Planning on Buying a New Car

A marketing research firm wishes to estimate the proportion of adults who are planning to buy a new car in the next 6 months. A simple random sample of 100 adults led to 22 who were planning to buy a new car in the next 6 months.

a. Compute the 95% confidence interval for the proportion of adults who are planning to buy a new a car in the next 6 months.
b. Interpret this confidence interval.
c. How large a sample size will need to be selected if we wish to have a 95% confidence interval that is accurate to within 1%.

Solution Preview

(a) Given:
p = 22/100 = 0.22
n = 100
z = 1.96
The 95% confidence interval for the proportion of adults who are planning to buy a new a car in the next 6 months is given as ...

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