Overview
1) The driving distance (in miles) to work for 30 people are as following:
12 9 7 2 8 7 3 27 21 10 13 7 2 30 7 6 13 6 4 1 10 3 13 6 2 9 2 12 16 18 Assume the population standard deviation is 8 miles. Find:
a) The point estimate of the population mean ?.
b) Construct a 95% confidence interval for the population mean
c) Interpret the results (Write a sentence).
d) Does it seem possible that the population mean could be greater than 12.5 miles? EXPLAIN.
2) This is U.S presidential election 2020.
Here is CNN poll the night before the election:
CANDIADTE A: 53%
CANDIDATE B: 47%
MARGIN OF ERROR : 4%
Assume the same percentages hold the next day, does candidate B has any shot of winning the election? OR is he/she pretty much lost the election & should congratulate candidate A?
EXPLAIN YOUR REASONING.
3) REPLY to a fellow classmate response (on question 2 only) , and comment on the validity of his/her response:
1) The driving distance (in miles) to work for 30 people are as following:
12 9 7 2 8 7 3 27 21 10 13 7 2 30 7 6 13 6 4 1 10 3 13 6 2 9 2 12 16 18 Assume the population standard deviation is 8 miles. Find:
a) The point estimate of the population mean ?.
Mean = sum(x)/n = 9.5
b) Construct a 95% confidence interval for the population mean
x bar +/- t(critical, alpha/2)*s/sqrt(n)
= 9.5 +/- 2.045*7.1907/sqrt(30) = (6.8, 12.2) miles
c) Interpret the results (Write a sentence).
We are 95% confident that the actual population mean is between the interval of 6.8 and 12.2 miles.
d) Does it seem possible that the population mean could be greater than 12.5 miles? EXPLAIN.
Yes, outliers are always possible, but they are unusual because they lie in the rejection region (greater than 2 standard deviations from the mean) which represents only 5% of the samples.
2) This is U.S presidential election 2020.
Here is CNN poll the night before the election:
CANDIADTE A: 53%
CANDIDATE B: 47%
MARGIN OF ERROR : 4%
Assume the same percentages hold the next day, does candidate B has any shot of winning the election? OR is he/she pretty much lost the election & should congratulate candidate A? EXPLAIN YOUR REASONING.
Candidate A with margin of error: (49%, 57%)
Candidate B with margin of error: (43%, 51%)
Candidate B definitely has a shot since the two candidates have overlapping confidence intervals. The two candidates are in a statistical dead heat within the margin of error.