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

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

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".

represent the sample mean for the sample  

population mean (variable of interest)

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:

  (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(0.025,4)".And we see that

So the correct option would be:

B. 2.7764