Final answer:
To construct a 95% confidence interval for the proportion of basketball fans from Florida that prefer watching college basketball, calculate the point estimate and error bound. The point estimate is obtained by dividing the number of fans who prefer college basketball by the total sample size. The error bound is calculated using the critical value and standard error.
Step-by-step explanation:
To construct a 95% confidence interval for the proportion of basketball fans from Florida that prefer watching college basketball, we first need to find the point estimate and the error bound.
a. The point estimate is the sample proportion, which is calculated by dividing the number of fans who prefer watching college basketball (260) by the total number of fans surveyed (400):
Point Estimate = 260/400 = 0.65
The error bound is calculated using the formula:
Error Bound = Critical Value * Standard Error
Since we are constructing a 95% confidence interval, the critical value is 1.96 (obtained from the z-table).
The standard error is calculated using the formula:
Standard Error = sqrt((Point Estimate * (1 - Point Estimate)) / Sample Size)
Substituting the values we have:
Standard Error = sqrt((0.65 * (1 - 0.65)) / 400) = 0.025
Therefore, the error bound is:
Error Bound = 1.96 * 0.025 = 0.049
So, the 95% confidence interval for the proportion of basketball fans from Florida that prefer watching college basketball is:
0.65 ± 0.049