Question

A random sample of 20 dirt bikes have a mean fuel capacity of 1.91 gallons with a standard deviation of 0.74 gallons. At the 10% level of significance, do the data provide sufficient evidence to conclude that the mean fuel tank capacity of all dirt bikes is 2 gallons? Assume that the population of fuel capacity is normally distributed.

(use the critical value approach and the P-value approach-show calculations).

Answer 1

Since the sample size is 20<30 hence here t-statistic is applicable here, so,

The hypotheses are:

level of significance is 10% and the two-tailed test is applicable here

Rejection region:

Reject Ho if |T_obs|>t_0.05,19, where Degree of Freedom=n-1=20-1=19

Test statistic:

The test statistic is calculated as

P-value:

P value associated with the T observed value is

0.5<P-value<0.5

Conclusion:

Since |T_obs|<t_0.05,19 and P-value >0.10 hence we fail to reject the null hypothesis and conclude that there is not enough evidence to support that the mean differs from 2.