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Hypothesis Testing: Mean, Population proportion & ANOVA
See data file attached.
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. If you calculate the answers manually, be sure to show your work. I would prefer a Word document with your answers below each problem, but you may also submit an Excel document.
1: 10.20 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) What is your decision on the null hypothesis? 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: 10.44: 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. Do you reject the null hypothesis of no difference? (c) Is normality assured? Why or why not? (d) Is the difference large enough to be important?
3: 11.24 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) If there is at least one significant difference among the groups, are there any significant differences between pairs of groups? What multiple comparison 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
Directions: For the following hypothesis tests, identify the null and alternative hypothesis, and the critical value. Then, calculate the test statistic, note the p value and make a decision on the null hypothesis. Please show your work if you calculated manually. If you used statistical software, please show output. Your p value will be approximate if you use manual calculation (i.e., less than .05) or exact (if you used statistical software).
1. Hypothesis test for the difference of population means: t test
A purchasing manager for a large university is investigating which brand of LCD projector to purchase to equip "smart" classrooms. Of major concern is the longevity of the light bulbs used in the projectors. The purchasing manager has narrowed down the choice of projector to two brands, Infocus and Proxima, and wishes to determine if there is any difference between the two brands in the mean lifetime of the bulbs used.
The purchasing manager obtained thirteen projectors of each brand for testing over the last several academic terms. The number of hours the bulbs lasted on each of the thirteen machines is given in the table.
Infocus Proxima
762 900
954 720
854 1132
935 631
861 690
908 1112
890 732
1012 754
964 1032
807 865
1013 953
798 754
923 778
Assume that the two populations of lifetimes are normally distributed and that the population variances are equal. Can we conclude, at the 0.01 level of significance, that there is a difference in the mean lifetime of the light bulbs in the two brand
2. Hypothesis test for the difference of population means: ANOVA
The manager of a computer software company wishes to study the number of hours senior executives spend at their desktop computers by type of industry. The manager selected a sample of five executives from each of three industries. At the .05 significance level, can she conclude there is a difference in the mean number of hours spent per week by industry?
Banking Retail Insurance
10 7.5 8
11 7 8.5
9 5 8
8 5 5
10 6 7
Answers:
1: State the null & alternative hypothesis:
2: Identify critical value
3: Calculate test statistic
(p value)
4: State your decision on H0
5: If you reject H0, identify groups that are significantly different from each other.
Answers:
1: State the null & alternative hypothesis:
2: Identify critical value
3: Calculate test statistic
(p value)
4: State your decision on H0