Question

use the results from a survey of a simple random sample of 1166 adults. among the 1166 respondents, 82% rated themselves as above average drivers. we want to test the claim that \\( \frac { 17 } { 20 } \\) 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
\\( \square = \square \\)
(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.
\\( \square = \square \\)
(type an integer or a decimal rounded to two decimal places as needed.)

Explanation:

Step1: Calculate the actual number of respondents (part a)

To find the number of respondents who rated themselves as above - average drivers, we use the formula \(n = N\times p\), where \(N = 1166\) (sample size) and \(p=0.82\) (proportion of respondents who rated themselves as above - average drivers).

$$n=1166\times0.82 = 1166\times\frac{82}{100}=1166\times0.82 = 956.12\approx956$$

Step2: Identify the sample proportion (part b)

The sample proportion \(\hat{p}\) is the proportion of the sample that has a certain characteristic. Here, \(\hat{p}=0.82\) (given as \(82\%\) in the problem). The symbol for the sample proportion is \(\hat{p}\), so \(\hat{p}=0.82\)

Step3: Identify the population proportion (part c)

The claim is that \(\frac{17}{20}\) of adults rate themselves as above - average drivers. We convert \(\frac{17}{20}\) to a decimal. \(\frac{17}{20}=17\div20 = 0.85\). The symbol for the population proportion is \(p\), so \(p = 0.85\)

Answer:

a. \(956\)
b. \(\hat{p}=0.82\)
c. \(p = 0.85\)