# 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

#### Solution Summary

The solution provides step by step method for the calculation of testing of hypothesis of mean, population proportion and ANOVA. 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.