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Chapter 8: Q1BSC (page 356)

In Exercises 1鈥�4, use these results from a USA Today survey in which 510 people chose to respond to this question that was posted on the USA Today website: 鈥淪hould Americans replace passwords with biometric security (fingerprints, etc)?鈥� Among the respondents, 53% said 鈥測es.鈥� We want to test the claim that more than half of the population believes that passwords should be replaced with biometric security.

Number and Proportion

a. Identify the actual number of respondents who answered 鈥測es.鈥�

b. Identify the sample proportion and the symbol used to represent it.

Short Answer

Expert verified

a.The actual number of respondents who answered 鈥測es鈥� is equal to 270.

b. The proportion of respondents who answered 鈥測es鈥� in the given sample is referred to as the sample proportion and is equal to 0.53.

The symbol used to represent the sample proportion is \(\hat p\).

Step by step solution

01

Given information

It is given that out of 510 people who responded to a survey, 53% said 鈥測es鈥� to the question of whether they should replace passwords with biometric security.

02

Identify the actual number of respondents who replied with “yes”

a.

The total sample size (n) is equal to 510.

The proportion of respondents who answered 鈥測es鈥� is equal to 53%.

The actual number of respondents who answered 鈥測es鈥� is computed below:

\(\begin{array}{c}53\% \;of\;510 = 53\% \times 510\\ = \frac{{53}}{{100}} \times 510\\ = 270.3\\ \approx 270\end{array}\)

Therefore, the number of respondents who answered 鈥測es鈥� is equal to 270.

03

Sample proportion

b.

The proportion of respondents who answered 鈥測es鈥� in the given sample is referred to as the sample proportion.

The symbol used to represent the sample proportion is\(\hat p\).

Thus,

\(\begin{array}{c}\hat p = 53\% \\ = 0.53\end{array}\).

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