Problem 5 (25 points, 5 points for Parts 1 to 3 and 10 points for Part 4 ). The

Question

Problem 5 (25 points, 5 points for Parts 1 to 3 and 10 points for Part 4 ). The nominal power
produced by a student-designed internal combustion engine is 100 hp. The student team that
designed this engine conducted 5 tests to determine the actual power. The data are: 99, 102, 100,
104, and 100.
Part 1. Find the sample mean.

Part 2. Find the sample variance.
Part 3. Assume that the nominal mean is true. Find the t-statistic and it degrees of freedom.
Part 4. Normality assumption can be checked with Q-Q plot. The ordered data are:
y(1)=99, y(2)=100, y(3)=100, y(4)=102, y(5)=104. Find P(4)- the estimated cumulative
probability point for y(4), and q(4)- the corresponding normal quantile of P(4)

Explanation / Answer

Sample mean = 101

Sample Variance = 4, std. dev. = 2

Degrees of freedom = 4

test statistics t,

t = (101 - 100)/(2/sqrt(5)) = 1.1180

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