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Chapter 8: Q1 (page 373)

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.

Short Answer

Expert verified

a. The actual 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 and is equal to 0.53.

The symbol used to represent the sample proportion isp^

Step by step solution

01

Given information

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.

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 “yes” is equal to 53%.

The actual number of respondents who answered “yes” is computed below:

53%of510=53%×510=53100×510=270.3≈270

Therefore, the number of respondents who answered “yes” is equal to 270.

03

Sample proportion

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 p^.

Thus,

p^=53%=0.53

.

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Most popular questions from this chapter

P-Values. In Exercises 17–20, do the following:

a. Identify the hypothesis test as being two-tailed, left-tailed, or right-tailed.

b. Find the P-value. (See Figure 8-3 on page 364.)

c. Using a significance level of α = 0.05, should we reject H0or should we fail to reject H0?

The test statistic of z = 2.01 is obtained when testing the claim that p≠0.345.

Using Confidence Intervals to Test Hypotheseswhen analyzing the last digits of telephone numbers in Port Jefferson, it is found that among 1000 randomly selected digits, 119 are zeros. If the digits are randomly selected, the proportion of zeros should be 0.1.

a.Use the critical value method with a 0.05 significance level to test the claim that the proportion of zeros equals 0.1.

b.Use the P-value method with a 0.05 significance level to test the claim that the proportion of zeros equals 0.1.

c.Use the sample data to construct a 95% confidence interval estimate of the proportion of zeros. What does the confidence interval suggest about the claim that the proportion of zeros equals 0.1?

d.Compare the results from the critical value method, the P-value method, and the confidence interval method. Do they all lead to the same conclusion?

P-Values. In Exercises 17–20, do the following:

a. Identify the hypothesis test as being two-tailed, left-tailed, or right-tailed.

b. Find the P-value. (See Figure 8-3 on page 364.)

c. Using a significance level of α= 0.05, should we reject or should we fail to reject ?

The test statistic of z = 1.00 is obtained when testing the claim that p>0.3.

Critical Values. In Exercises 21–24, refer to the information in the given exercise and do the following.

a. Find the critical value(s).

b. Using a significance level of = 0.05, should we reject H0or should we fail to reject H0?

Exercise 17

Testing Claims About Proportions. In Exercises 9–32, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, or critical value(s), then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. Use the P-value method unless your instructor specifies otherwise. Use the normal distribution as an approximation to the binomial distribution, as described in Part 1 of this section.

Survey Return Rate In a study of cell phone use and brain hemispheric dominance, an Internet survey was e-mailed to 5000 subjects randomly selected from an online group involved with ears. 717 surveys were returned. Use a 0.01 significance level to test the claim that the return rate is less than 15%.
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