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Hypothesis Testing of Mean & Proportion

Ford Motor Company wishes to estimate the mean dollar amount of damage done to a new model Taurus as a result of a 10 mph crash into the rear bumper of a parked car. 36 Tauruses are test crashed into parked cars and the dollar amount of damage done to each is recorded. The results are:

a. Does the sample data provide evidence that the population mean amount of damage is less than $475 (using =0.05)? Use the 5 step hypothesis testing procedure.

1. Formulate the null and alternative hypotheses.
2. Determine the criterion for rejection or non-rejection of the null hypothesis. That is, determine the Z critical value.
3. Calculate the Z test statistic.
4. Compare the Z test statistic to the Z critical value (rejection region) and make a judgment about the null and alternative hypotheses.
5. Interpret the statistical decision in terms of the problem.
6. Compute the observed p value in the hypothesis test, and interpret this value. What does this mean?

A random sample of 300 beer drinkers is selected and each member of the sample is asked to choose between two beers: Brand A and Brand B. The results are that 165 prefer brand A and 135 prefer brand B.

a. Does the sample data provide evidence to conclude that more than 50% of the population of beer drinkers prefer brand A to brand B (using =0.01)? Use the 5 step hypothesis testing procedure.

p = population proportion favoring brand A.

1. Formulate the null and alternative hypotheses:
2. Determine the criterion for rejection or non-rejection of the null hypothesis. That is, determine the Z critical value.
3. Calculate the Z test statistic.
4. Compare the Z test statistic with the Z critical value (rejection region) and make a judgment about the null and alternative hypotheses:
5. Interpret the statistical decision in terms of the problem.
6. Compute the observed p value in the hypothesis test, and interpret this value. What does this mean?

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Solution Summary

The solution provides step by step method for the calculation of testing of hypothesis. 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.

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