writer = c(rep(\"CD-Writer\", 17), rep(\"No CD-Writer\", 23)) batterytime =c(3.6

Question

writer = c(rep("CD-Writer", 17), rep("No CD-Writer", 23))
batterytime =c(3.69, 4.45, 5.33, 4.10, 4.94, 4.27, 4.96, 3.60, 5.23, 3.94,
               4.20, 5.70, 5.06, 3.66, 5.26, 5.64, 5.41, 5.64, 4.64, 4.29,
               6.24, 4.99, 3.95, 5.36, 5.57, 6.28, 5.17, 4.81, 6.00, 4.54,
               4.43, 4.87, 4.74, 5.01, 6.06, 4.93, 5.28, 4.43, 4.76, 5.14)

Researchers would like to know whether there is a significant difference between the average battery life of laptops with a CD writer and those without. To understand the effect of CD writing on laptop batteries, 23 users without a CD writer and 17 users with a CD writer are asked to work on their laptops until the "low battery" sign came on. The following software output is an analysis of this data: Std. Dev. Possible Effect of CD Writers on Laptop Batteries Mean 23 No CD Writer 5.09 0.64 17 0.72 CD Writer 4.67 Welch Two Sample t-test data: batterytime by writer t 1.9095, df 31.902, p-value 0.06523 alternative hypothesis: true difference in means is not equal to C 90 percent confidence in terval -0.79198476 -0.04735027 sample estimates: mean in group CD-Write r mean in group No co-writer 3.5 40 45 50 55 00 4.672941 5.092609 Battery Time in Hours Do these data provide evidence of a difference between the average battery life of laptops with a CD writer and those without? Assume data is obtained randomly. Use a significance level of 0.10 and answer the following questions using the software output. a. (2 points) Is there visual evidence that the average battery life is different among the laptops with and without the CD writer? Explain. b. (2 points State the null and alternative hypothesis to answer the question of interest. Is the test one or two sided? c. (1 points) Check conditions for the test. State each and whether it is met d. (5 points) Using the R output give a four part conclusion and thoroughly answer the question of interest

Explanation / Answer

a. By studying the descriptive output, and the box plot, it seems that there is difference in mean battery life of among laptops with and without the CD writer (Mean battery life for laptop with CD writer is:4.67, and mean battery life for laptop without CD writer is:5.09).

b. Null hypothesis, H0:mucd-muno-cd=0 (there is no difference in mean battery life of laptops with and without CD writer)

Alternative hypothesis, H1:mucd-muno-cd=/=0 (there is difference in mean battery life of laptops with and without CD writer).

c. Randomization condition: This is an experiment, the data has been obtained randomly, therefore, the randomization condition is met.

Independent group assumption: the data being collected randomly, the battery life of laptops with CD writer is independent of battery life of laptops without CD writer.

Independence assumption: This being an experiment, there is no need that subjects are to be chosen randomly from a population, all they need is to be assigned randomly to groups.

Nearly normal condition: the two groups of data are roughly normal.

d. 1. Hypotheses:

H0:mucd-muno-cd=0 (there is no difference in mean battery life of laptops with and without CD writer)

H1:mucd-muno-cd=/=0 (there is difference in mean battery life of laptops with and without CD writer).

2. Test statistic.

t=-1.9095

3. Compute P value.

p value at 31.902 df is :0.06523

4. Conclusion.

Per rule, reject H0, if p value is less than given significance level. Here, p value is less than 0.10, therefore, reject H0, and conclude that there is significant difference in mean battery life of laptops with a CD writer and without a CD writer.

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