For the following questions, first state whether the test needed is a Z-statistic or T-statistic and calculate the

test statistic.

Note: Feel free to make a new cell to do some calculations with Python if need be.

a. The grades on a statistics test at GW University are normally distributed with μ = 55 and σ = 12. George scored G = 65 on the exam. You want to test whether George’s score is more than the mean.

b. The heights of the statisticians working on the Large Hadron Collider project seems to be normally distributed with μ = 68 inches and σ = 5 inches. Dr. Numbercrackers’ height is H = 61 inches. You want to test is Dr. Numbercracker’s height is different from the mean.

c. The Bureau on Economic Development conducted a survey of families residing in a small town of Gugelshnackel. 100 residents were surveyed and the survey revealed that X ̄ = 45, 000 and s = 10, 538. You need to test whether mean income is statistically different from a null hypothesis of 40,000. 

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