Answer:
i)
The confidence interval is at 90%
ii)
The margin of error is 5%
iii)
The 90% confidence interval is (70%, 80%)
iv)
We are 90% confident that the average score of seniors in the field test is between 70% and 80%.
Step-by-step explanation:
i)
The confidence interval is at 90%
We are informed that the exam creator claims that on this particular exam, nine times out of ten, seniors will have an average score within 5% of 75%. This implies that we are 9 times out of 10 confident that seniors will have an average score within 5% of 75%.
The level of confidence is thus;
(9/10)*100 = 90%
ii)
The margin of error is 5% or equivalently 0.05
We are informed that the exam creator claims that on the same exam, nine times out of ten, seniors will have an average score within 5% of 75%.
Since the average score is within 5%, the margin of error is 5%
iii)
A confidence interval is calculated using the formula;
point estimate ± margin of error
Our point estimate is 75%
Our margin of error is 5%
The 90% confidence interval is thus;
75% ± 5% = (70%, 80%)
iv)
The 90% confidence interval is interpreted as;
We are 90% confident that the average score of seniors in the field test is between 70% and 80%.
This is a confidence interval for the mean, the level of confidence is 90% and our confidence interval is (70%, 80%).
