In Exercises 1–4, 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: “Should Americans replace passwords with biometric security (fingerprints, etc)?” Among the respondents, 53% said “yes.” 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 “yes.”

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

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

a.

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

The proportion of respondents who answered “yes” is equal to 53%.

The actual number of respondents who answered “yes” 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 “yes” is equal to 270.

b.

The proportion of respondents who answered “yes” in the given sample is referred to as the sample proportion.

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

Thus,

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