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 all conditions for inference have been met. Based on the confidence interval, which of the following claims 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

Answer:

b. More than half of all people prefer texting.

Step-by-step explanation:

According to the survey 56% of the respondents prefer texting over making call. This means the value of sample proportion p is:

Sample proportion = p = 56% = 0.56

The margin of error with 95% confidence interval is 3 percent points i.e.

Margin of error = M.E = 0.03

The true value of the population proportion can be expressed as the following confidence interval:

From p - M.E to p + M.E

Lower Limit = p - M.E = 0.56 - 0.03 = 0.53 = 53%

Upper Limit = p + M.E = 0.56 + 0.03 = 0.59 = 59%

From here we can see that the lower and upper limit of confidence interval are above 50%. Based on these calculations the following claim can be supported:

b. More than half of all people prefer texting.