1) Each person in a random sample of 900 city residents was asked if he or she s
ID: 3055435 • Letter: 1
Question
1)
Each person in a random sample of 900 city residents was asked if he or she supports having a skateboard park built in the city. The results are shown below.
Support 47%
Oppose 45%
No opinion 8%
The margin of error for the estimate of the percentage who support building the skateboard park is 3 percentage points. Which of the following statements is most appropriate given the survey results?
A. Plausible values for the actual percentage of city residents who support building the skateboard park are those between 44% and 50%.
B. It is likely that 3% of the sample (27 city residents) answered the question incorrectly.
C. There is a 97% probability that the percentage of city residents who support having the skateboard park built is 47%.
D. It would be unlikely to observe 47% support in the sample if the actual percentage of city residents who support building the skateboard park is 45%.
E. Choices (A), (B), and (D) are all correct.
2)Express the confidence interval 18.9%±5.4%18.9%±5.4% in interval form.
______ Enter in interval notation. Do not enter as a percent.
3 )
If n=400 and ˆpp^ (p-hat) =0.86, find the margin of error at a 99% confidence level.
________ Round to 4 places.
z-scores may be rounded to 3 places or exact using technology.
If n=570 and ˆpp^ (p-hat) = 0.07, construct a 99% confidence interval.
Give your answers to three decimals. ______< P < _____
4)
You want to obtain a sample to estimate a population proportion. At this point in time, you have no reasonable estimate for the population proportion. Your would like to be 98% confident that you estimate is within 4% of the true population proportion. How large of a sample size is required?
n = _______
Do not round mid-calculation. However, use a critical value accurate to three decimal places.
Explanation / Answer
Solution:
1) We are given that :
Each person in a random sample of 900 city residents was asked if he or she supports having a skateboard park built in the city. The results are shown below.
Support 47% Oppose 45% No opinion 8%
The margin of error for the estimate of the percentage who support building the skateboard park is 3 percentage points.
That is : E = 3%
Margin of Error is the half width of confidence interval , by using margin of error we can find confidence interval.
We do not look for a point estimate by using Margin of error.
thus confidence interval for true proportion is :
( p^ - E < p < p^ + E )
( 47% - 3% < p < 47% + 3% )
( 44% < p < 50% )
Thus correct statement is A) plausible values for the actual percentage of city residents who support building the skateboard park are those between 44% and 50%.
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