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britt729
07.03.2020 •
Mathematics
As part of a study of the development of the thymus gland, researchers weighed the glands of five chick embryos after 14 days of incubation. The thymus weights (mg) were as follows:
41.5, 39.2, 41.2, 42.3, 41.3.
Assume that thymus gland weight of chick embryos follow normal distribution. If you were to construct a 95 percent confidence interval for the mean thymus gland weight, it would take the form:
(sample mean) +/- t.quantile * (standard error of sample mean)
What is the correct value of t.quantile for a 95 percent confidence interval in this study?
A. 2.1319
B. 2.7764
C. 2.5706
D. 1.96
E. 2.0150
Solved
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Ответ:
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(0.025,4)".And we see that ![t_{\alpha/2}=2.7764](/tpl/images/0537/4403/67125.png)
So the correct option would be:
B. 2.7764
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".
s represent the sample standard deviation
n represent the sample size
Solution to the problem
The confidence interval for the mean is given by the following formula:
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(0.025,4)".And we see that ![t_{\alpha/2}=2.7764](/tpl/images/0537/4403/67125.png)
So the correct option would be:
B. 2.7764
Ответ: