Assignment:
Directions: You may include the statistical software output, but you must also include a well-written explanation of the findings. Be sure to answer the question asked in each problem, and explain why, with reference to your output.
Q1. 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?
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Cell Phone Battery Life Experiment (n = 10)
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Participant
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New Battery
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Old Battery
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Bob
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45
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52
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May
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41
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34
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Deno
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53
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40
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Sri
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40
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38
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Pat
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43
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38
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Alexis
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43
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44
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Scott
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49
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34
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Aretha
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39
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45
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Jen
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41
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28
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Ben
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43
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33
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Q2: 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?
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Hypothesis test for two independent proportions
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p1
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p2
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pc
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0.0237
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0.0409
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0.0322
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p (as decimal)
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58/2450
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97/2370
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155/4820
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p (as fraction)
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58.
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97.
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155.
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X
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2450
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2370
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4820
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n
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-0.0173
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difference
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0.
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hypothesized difference
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0.0051
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std. error
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-3.39
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z
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.0003
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p-value (one-tailed, lower)
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-0.0272
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confidence interval 95.% lower
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-0.0073
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confidence interval 95.% upper
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0.01
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half-width
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Q3: 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.
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Crash Damage in Dollars
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Goliath
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Varmint
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Weasel
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1100
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1290
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1100
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750
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1400
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1500
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970
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1390
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1000
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1000
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1850
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1250
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850
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1100
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1920
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