Question

A recent survey of cell phone users indicated that 56 percent of the respondents prefer to use cell phones for texting rather than for making phone calls. A 95 percent confidence interval for the estimate of all cell phone users who prefer to use cell phones for texting has a margin of error of 3 percent.

Assume al contions for inference have been met. Based on the confidence where which of the following claim is supported?

A. Less than half of all people prefer texting
B. More than half of all people prefer texting
C. At least 60 percent of all people prefer texting
D. At least 75 percent of all people prefer texting
E. At least 95 percent of all people prefer texting

Answer 1

Given Information:

mean = μ = 56%

margin of error = σ = 3%

Confidence Level = 95%

Required Information:

Range of mean with 95% confidence Level = ?

Answer:

Range of mean with 95% confidence Level = 50% to 62%

Explanation:

We know that within 95 % confidence interval, the data will fall within 2 standard deviations from the mean

μ ± 2σ

We have mean μ = 0.56 and standard error σ = 0.03

0.56 + 2*0.03 and 0.56 - 2*0.03

0.56 + 0.06 and 0.56 - 0.06

0.62 and 0.50

or

50% to 62%

Conclusion:

Since the percentage is 50 or greater, option B best fits the scenario, more than half of all people prefer texting

We are 95% confidence that 50 to 62 % of the the respondents prefer to use cell phones for texting rather than for making phone calls.

Answer 2

(B) More than half of all people prefer texting.

Explanation:

Confidence interval for a proportion is given as sample proportion +/- margin of error

sample proportion (p) = 56%

margin of error (E) = 3%

Lower limit = p - E = 56% - 3% = 53%

Upper limit = p + E = 56% + 3% = 59%

The percentage of half of all people is 50%

95% confidence interval of the proportion of all people who prefer texting is (53%, 59%). This interval shows that more than half of all people prefer texting.