Problem

from a survey of a simple random sample of 1009 adults. Among the 1009 respondents, $76 \%$ rated them the claim that $\frac{13}{20}$ 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. $\nabla=$ (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 :First, we need to find the actual number of respondents who rated themselves as above average drivers. This can be done by multiplying the total number of respondents (1009) by the percentage of respondents who rated themselves as above average drivers (76%). This gives us \(1009 \times 0.76 = 767\).

Step 2 :Next, we need to find the sample proportion. This is simply the percentage of respondents who rated themselves as above average drivers, expressed as a decimal. So, we divide the percentage by 100 to get \(\frac{76}{100} = 0.76\).

Step 3 :Finally, we need to find the population proportion. This is given as \(\frac{13}{20} = 0.65\). This is the proportion of all adults (not just those in the sample) who rate themselves as above average drivers.

Step 4 :So, the actual number of respondents who rated themselves as above average drivers is \(\boxed{767}\), the sample proportion is \(\boxed{0.76}\), and the population proportion is \(\boxed{0.65}\).

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Source: https://solvelyapp.com/problems/18772/

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