Graph the following inequality. Then click to show the correct graph. y ≤ -2
2 answers:
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Answer:
D. Matthew's estimate will have the smaller margin of error because the larger sample size more than compensates for the higher level of confidence
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of , and a confidence interval
, we have the following confidence interval of proportions.
In which
z is the zscore that has a pvalue of .
The margin of error is the division by 2 of the upper level of the interval by the lower level
, so this is
Both Katrina and Matthew are working with the same population, so is equal for both.
Katrina
Katrina wants to estimate the proportion of adults who read at least 10 books last year. To do so, she obtains a simple random sample of 100 adults and constructs a 95% confidence interval. This means that she has and
. So her margin of error is
Matthew
He obtains a simple random sample of 400 adults and constructs a 99% confidence interval.
This means that, for Matthew, . So his margin of error is:
Higher confidence levels usually led to higher margins of error. However, Matthew's larger sample size compensates his higher confidence level.
So the correct answer is:
D. Matthew's estimate will have the smaller margin of error because the larger sample size more than compensates for the higher level of confidence