AimettiA8J

2022-12-04

A random sample of residents in city J were surveyed about whether they supported raising taxes to increase bus service for the city. From the results, a 95 percent confidence interval was constructed to estimate the proportion of people in the city who support the increase. The interval was (0.46,0.52)(0.46,⁢0.52).
Which of the following claims is supported?
A) More than 90 percent of the residents support the increase.
B) More than 60 percent of the residents support the increase.
C) More than 40 percent of the residents support the increase.
D) Fewer than 10 percent of the residents support the increase.
E) Fewer than 25 percent of the residents support the increase.

Dangelo Cain

Expert

The confidence interval at 100 $\left(1–\alpha \right)$% confidence level gives us an interval estimate about the population parameter. Alpha is the significance level. Express our confidence that, if several such samples are collected, then about 100 $\left(1–\alpha \right)$ % of those samples would yield 100 $\left(1–\alpha \right)$ % level confidence intervals that would contain the true population parameter. The confidence level here is 95%. The confidence interval is (0.46, 0.52). So, the actual proportion of people in the city, who support the increase is more than 0.40. So, it can be said with 95% confidence that more than 40% of the residents support the increase.