# Hypothesis Testing: Mean & Variance

See the attached file.

2(a). In the context of hypothesis test, state what is meant by:

(i). Type I error

(ii). Type II error

(iii). Power of the test

What connections are there, if any, between them?

(b). The sales and marketing team in motor business is investigating the quality of second hand cars. One indicator of quality is the number of miles on the clock. The following table gives the summary statistics of the miles on the clock for two different engine size models.

Sample size Mean Standard deviation

Model 1.8 10 8840 1928

Model 1.4 8 6180 920

(i) Using a 1% level of significance, test whether there is any significant difference in the variances between the two models.

(ii) Test the hypothesis that the average mileage for model 1.8 is greater than for model 1.4 at the 1% level of significance and interpret your results.

See attached.

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#### Solution Summary

The solution provides step-by-step method for the calculation of testing of hypothesis. The solution also provides the definition of Type I error, Type II error and power of test. Formula for the calculation and Interpretations of the results are also included. Interactive Excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.