Question

Use the sample data and confidence level given below to complete parts? (a) through? (d). A research institute poll asked respondents if they felt vulnerable to identity theft. In the? poll, n equals 1070 and x equals 572 who said? "yes." Use a 95 % confidence level. LOADING... Click the icon to view a table of z scores. ?a) Find the best point estimate of the population proportion p. nothing ?(Round to three decimal places as? needed.) ?b) Identify the value of the margin of error E. Eequals nothing ?(Round to three decimal places as? needed.) ?c) Construct the confidence interval. nothingless than p less than nothing ?(Round to three decimal places as? needed.) ?d) Write a statement that correctly interprets the confidence interval. Choose the correct answer below. A. 95?% of sample proportions will fall between the lower bound and the upper bound. B. One has 95?% confidence that the sample proportion is equal to the population proportion. C. There is a 95?% chance that the true value of the population proportion will fall between the lower bound and the upper bound. D. One has 95?% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion.

Answer #1

The statistical software output for this problem is:

**One sample proportion summary confidence
interval:**

p : Proportion of successes

Method: Standard-Wald

**95% confidence interval results:**

Proportion |
Count |
Total |
Sample Prop. |
Std. Err. |
L. Limit |
U. Limit |
---|---|---|---|---|---|---|

p | 572 | 1070 | 0.53457944 | 0.015248847 | 0.50469225 | 0.56446663 |

Hence,

a) Point estimate = 0.535

b) Margin of error = (0.564 - 0.505)/2 = 0.030

c) 95% confidence interval: (0.505, 0.564)

d) One has 95% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion.

**Option D** is correct.

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