Question

use the results from a survey of a simple random sample of 1064 adults. among the 1064 respondents, 84% rated themselves as above average drivers. we want to test the claim that \\( \frac{4}{5} \\) 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.
894
(round to the nearest whole number as needed.)
b. identify the sample proportion and use the symbol that represents it.
\\( \hat{p} \\) = 84
(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.
\\( p \\) = 80
(type an integer or a decimal rounded to two decimal places as needed.)

Explanation:

Step1: Calculate the actual number of respondents

The formula for calculating the number of respondents who rated themselves as above - average drivers is \(n\times p\), where \(n = 1064\) (sample size) and \(p=0.84\) (sample proportion).

$$1064\times0.84 = 893.76\approx894$$

Step2: Identify the sample proportion symbol and value

The sample proportion is denoted by \(\hat{p}\). Given that \(84\%\) of the sample rated themselves as above - average drivers, \(\hat{p}=0.84\)

Step3: Identify the population proportion symbol and value

The claim is that \(\frac{4}{5}\) of adults rate themselves as above - average drivers. Since \(\frac{4}{5}=0.8\), and the population proportion is denoted by \(p\), so \(p = 0.80\)

Answer:

a. \(894\)
b. \(\hat{p}=0.84\)
c. \(p = 0.80\)