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

Given Information:

mean = μ = 56%

margin of error = σ = 3%

Confidence Level = 95%

Required Information:

Range of mean with 95% confidence Level = ?

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

Step-by-step 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.

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