1) Construct a 95% confidence interval estimate for the population standard deviation, , of the annual salaries of software engineers if a sample of 14 randomly selected software engineers has a standard deviation of $3725.
a) Determine and .
b) Write down the formula and then calculate the confidence interval.
Follow the proper rounding rules.
For problems 2 – 5, test each claim by doing each of the following:
a) Identify the null and alternate hypotheses,
b) calculate the P-value,
c) state whether to reject or fail to reject H0,
d) state the conclusion about the claim.
2) A Pew Research poll of 328 randomly selected adults found that 62 of them stated that they used Instagram at least once a week. Use a 0.05 significance level to test the claim that more than 20% of adults use Instagram at least once a week.
3) In a 2020 survey of 600 motorcyclists, 404 wear a helmet. In another survey 500 motorcyclists taken a year earlier, 317 wore a helmet. Use a 0.01 significance level to test the claim that the proportion of motorcyclists who wear a helmet was greater in 2020.
4) The ages of randomly selected cars and taxis in Dublin Ireland is given below. Use a 0.05 significance level to test the claim that the mean age of cars is greater than the mean age of taxis.
Cars
4
0
8
11
14
3
4
4
3
5
8
3
3
7
4
6
6
1
8
2
15
11
Taxis
8
8
0
3
8
4
3
3
6
11
7
7
6
9
5
3
4
3
5) The number of hospital admissions from car accidents on Friday the 6th and Friday the 13th of the same month were randomly selected from hospital databases. Use a 0.05 significance level to test the claim that the number of admissions from car accidents is the same for Friday the 6th and Friday the 13th of the same month.
Friday the 6th
9
6
11
11
3
5
8
Friday the 13th
13
12
14
10
4
12
9
You have the option to do all your work by hand on your own paper and scan it, or you can type onto the document and submit it, or some combination. If you are unsure of anything, please contact me for clarification before the last minute. When you do your work, act as if you are trying to impress a potential employer.
