The answer is below hope it helps.
find two consecutive odd numbers such that the sum of the larger number and twice the smaller number is 27 less than four times
1 answer:
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Answer:
a)
So on this case the 99% confidence interval would be given by (13.83;28.17)
b)
c)
d) D. Decreasing the sample size increases the margin of error, provided the confidence level and population standard deviation remain the same.
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
Part a
represent the sample mean
population mean (variable of interest)
represent the population standard deviation
n=350 represent the sample size
99% confidence interval
The confidence interval for the mean is given by the following formula:
(1)
Since the Confidence is 0.99 or 99%, the value of and
, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.005,0,1)".And we see that
Now we have everything in order to replace into formula (1):
So on this case the 99% confidence interval would be given by (13.83;28.17)
Part b
The margin of error is given by:
Part c
The margin of error is given by:
Part d
As we can see when we reduce the sample size we increase the margin of error so the best option for this case is:
D. Decreasing the sample size increases the margin of error, provided the confidence level and population standard deviation remain the same.