The rate at which a fuel burns is an important feature of the fuel. A particular

Question

The rate at which a fuel burns is an important feature of the fuel. A particular type of fuel is supposedto have a mean rate of burning of 50 cm/s. We know the standard deviation of the rate is = 2 cm/s.Suppose you want to test whether the mean rate is 50 cm/s as specified or not. You have a randomsample of test data that includes n=25 samples, which produce a sample average burn rate of x =51.3 cm/s.

a.  If you use a level of significance of = 0.05, what conclusion should you draw? Do a hypothesis test to support your answer.

b. Compute the 95% confidence interval on average burn rate.

Explanation / Answer

a) Perform 1-sample Z test (population standard deviation is known).

Z=(Xbar-mu)/(sigma.sqrt n)

=(51.3-50)/(2/sqrt 25)

=3.25

p value is 0.0011. The p value is less than alpha=0.05. Reject H0 to conlude that mea rate is different from 50cm/s.

b) The 95% c.i=xbar+-Z(sigma/sqrt n)

=51.3+-1.96(2/sqrt 25)

=50.516 to 52.084

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