Using the Grubb's test, decide whether the value 217 should be rejected from the set of...

Using the Grubb's test, decide whether the value 217 should be rejected from the set of results 191, 217, 202, 205, 195.

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Expert Solution

We are required to use the Grubb's test for outliers in the above mentioned question.

First, we will be required to calculate the Grubb's statistic, and then measure it against the table value.

Our null hypothesis, H_o: 217 is not an outlier

Our alternate hypothesis, H_a: 217 is an outlier

The formula for the Grubb's statistic is:

Grubb's statistic= (absolute value of (value in question - mean of values))/ standard deviation of values

Let's first calculate the mean of values, and the standard deviation of values.

Mean of values= (191+217+202+205+195) / 5

= 202

Standard deviation of values= sqrt(((191-202)² + (217-202)² + (202-202)² + (205-202)² + (195-202)² ) / n-1)

= 10.04988

Thus, the Grubb's statistic is (217-202) / 10.04988

= 15 / 10.04988

= 1.49255

We can obtain the Grubb's test critical value from a Grubb's table.

Since no confidence level has been given, I am going to assume a confidence level of 95%.

At 95% level of confidence, and n=5, the Grubb's critical value is 1.672.

Since our Grubb's statistic < Grubb's critical value, we fail to reject the null hypothesis (or simply, accept the null hypothesis).

Thus, using the Grubb's test, 217 should NOT be rejected from the given set of results.

milcah answered 10 months ago

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