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Q4 20pts + bonus 5pts The following are the burning times (in minutes) of chemic

ID: 3306215 • Letter: Q

Question

Q4 20pts + bonus 5pts The following are the burning times (in minutes) of chemical flares of two different formulations. The design engineers are interested in both mean and variance of the burning times. Type 1: 65 81 57 66 82 82 67 59 75 70 Type 2: 64 71 83 59 65 56 69 74 82 79 (a) Assume that the two variances are equal. What other assumptions do you need to test the hypothesis that the mean burning times are equal? (b) Test the hypothesis that the rnean burning times are equal. Use a =0.05. (c) Construct a 95% confidence interval for 1 2, where 1 and 2 denote the population mean of the treatments Type 1 and Type 2, respectively. (d) (Bonus: 5pts) Test the hypothesis that the two variances are equal. Use = 0.05.

Explanation / Answer

Use R program to calculate these problem, the code is given and double click on R icon , write R program. the code is

>type1<-c(65,81,57,66,82,82,67,59,75,70) press enter key
> type2<-c(64,71,83,59,65,56,69,74,82,79) press enter key
> t.test(type1,type2,var.equal=T)

press enter key and the R code give the following output

Two Sample t-test

data: type1 and type2
t = 0.048008, df = 18, p-value = 0.9622
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-8.552441 8.952441
sample estimates:
mean of x mean of y
70.4 70.2

from the output since the p-value = 0.9622 is greater than level of significance alpha = 0.05 accept the null hypothesis.