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Hypothesis Test - Problems and Solutions

1. A new cell phone battery is being considered as a replacement for the current one. Ten college student cell phone users are selected to try each battery in their usual mix of "talk" and "standby" and to record the number of hours until recharge was needed. (a) Do these results show that the new battery has significantly longer life at α = .05? State your hypotheses and show all steps clearly. (b) Is the decision close? (c) Are you convinced?

Cell Phone Battery Life Experiment (n = 10)

Participant New Battery Old Battery
Bob 45 52
May 41 34
Deno 53 40
Sri 40 38
Pat 43 38
Alexis 43 44
Scott 49 34
Aretha 39 45
Jen 41 28
Ben 43 33

2. Does lovastatin (a cholesterol-lowering drug) reduce the risk of heart attack? In a Texas study, researchers gave lovastatin to 2,450 people and an inactive substitute to 2,370 people (average age 58). After 5 years, 58 of the lovastatin group had suffered a heart attack, compared with 97 for the inactive pill. (a) State the appropriate null and alternative hypotheses. (b) Interpret the results at α = .01. (c) Is normality assured? (d) Is the difference large enough to be important?

3. In a bumper test, three types of autos were deliberately crashed into a barrier at 5 mph, and the resulting damage (in dollars) was estimated. Five test vehicles of each type were crashed, with the results shown below. Research questions: (a) Are the mean crash damages the same or significantly different among these three vehicles? (b) Are there any significant differences between pairs of groups? What test did you use? Explain.

Crash Damage in Dollars

Goliath Varmint Weasel
1100 1290 1100
750 1400 1500
970 1390 1000
1000 1850 1250
850 1100 1920


Solution Summary

The solution provides step-by-step method of performing a hypothesis test. All the steps of hypothesis testing (formulation of null and alternate hypotheses, selection of significance level, choosing the appropriate test-statistic, decision rule, calculation of test-statistic and conclusion) have been explained in details. Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included.