Question

Fuel consumption: the standard deviation of the fuel consumption of a manufacturer's sport utility vehicle is hypothesized to be 3.3 miles per gallon. a random sample of 18 vehicles has a standard deviation of 2.8 miles per gallon. at a(alpha)=0.10, is the claim believable?

Answer 1

Given:

The Null Hypothesis:

H0 :

Alternate Hypothesis:

H1 :

Test Statistic:

Finding critical values:

Two tailed test, thus

dof = n-1 = 17

a) Upper cut critical value: value at

  

=27.587 (see image)

b) Lower cut critical value: at

= 8.672 (see image)

Decision Making:

Rule:

Reject null hypothesis if test statistic is less than lower cut critical value at given level of significance or if test statistic is more than upper cut critical value at given level of significance.

Here

thus:

and H0 is accepted.

Thus the claim is believable.

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