Suppose you doubt the assumption that the mean age of the stars is 3.3 billion y

Question

Suppose you doubt the assumption that the mean age of the stars is 3.3 billion years, but you don't know whether the true mean age is less or greater than 3.3 billion years.

A) To test whether the population mean is 3.3 billion years, what would your null and alternative hypotheses be?

B) What test will you use, how will the test work, and what are the conditions necessary to use the test? Does your situation meet those conditions?

C) Using the population and sample from question 2, calculate yoour test statistic and P-value. Show your work, including the formulas you used to calculate the statistic.

D) What's your conclusion, using a= .5? Compare your results to the previous conclusion, and explain the difference. Sketch the distribution of your sample mean, shading the area that represents your P-value. Label the value for the mean, label the values for the bounds of the shaded area.

Explanation / Answer

A)
H0: = 3.3
HA: 3.3
B)
z-test for mean (as we know the standard deviation and the ages are normally distributed)
The situation meets these conditions.
C)
Sample mean = 3.4
Standard deviation = 0.4
Standard error of mean = / n
Standard error of mean = 0.4 / 50
SE = 0.4/7.0711
Standard error of mean 0.0566
z = (xbar- ) / SE
z = (3.4-3.3) / 0.0566
z = 1.7678 -- test statistic
p-value = 2(0.0384) = 0.0768
D) using = .5 , since p-value < alpha, we reject the null hypothesis and conclude that the mean age is not equal to 3.3

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