Problem
Use the results from a survey of a simple random sample of 1277 adults. Among the 1277 respondents, $73 \%$ rated themselves as above average drivers. We want to test the claim that $\frac{7}{10}$ of adults rate themselves as above average drivers. Complete parts (a) through (c). a. Identify the actual number of respondents who rated themselves as above average drivers. (Round to the nearest whole number as needed.) b. Identify the sample proportion and use the symbol that represents it. $=$ (Type an integer or a decimal rounded to two decimal places as needed.) c. For the hypothesis test, identify the value used for the population proportion and use the symbol that represents it. \[ = \] (Type an integer or a decimal rounded to two decimal places as needed.)
Solution
Step 1 ：To find the actual number of respondents who rated themselves as above average drivers, we need to calculate 73% of 1277. This gives us \(0.73 \times 1277 = \boxed{932}\).
Step 2 ：The sample proportion is simply the actual number of respondents who rated themselves as above average drivers divided by the total number of respondents. This gives us \(\frac{932}{1277} = \boxed{0.73}\).
Step 3 ：The population proportion for the hypothesis test is given as \(\frac{7}{10}\) or \(\boxed{0.7}\).
