Which expression has a value of 32 when m = 8?
2 answers:
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Answer:
a)
And we can conclude that we are 95% confident that the true mean of Co2 level is between 608.29 and 700.03 ppm
b)
Step-by-step explanation:
Part a
The confidence interval for the mean is given by the following formula:
(1)
In order to calculate the critical value we need to find first the degrees of freedom, given by:
Since the Confidence is 0.95 or 95%, the value of and
, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,51)".And we see that
Replacing we got:
And we can conclude that we are 95% confident that the true mean of Co2 level is between 608.29 and 700.03 ppm
Part b
The margin of error is given by :
(a)
The desired margin of error is ME =50/2=25 and we are interested in order to find the value of n, if we solve n from equation (a) we got:
(b)
The critical value for 95% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.025;0;1)", and we got , and we use an estimator of the population variance the value of 175 replacing into formula (b) we got: