Question

The deflection temperature under load for two different types of plastic pipe is being investigated. Two random samples of 12 pipe specimens are tested, and the deflection temperatures observed are shown as follows (in °F):

Type-1 206   188   205   187   196   192   185   213   192   194   178   205

Type-2 177   197   206   201   180   176   185   200   197   193   198   188

a. Use Excel/R to compute the sample mean and sample variance of each type.

b. Do the data support the claim that the deflection temperature under load for type 1 pipe exceeds that of type 2 at 5 % level of significance? (assume population standard deviation are equal)

Answer 1

type1<- c(206,188,205,187,196,192,185,213,192,194,178,205)
> type2<- c(177,197,206,201,180,176,185,200,197,193,198,188)
>
> #To calculate sample mean :
>
> mean(type1)
[1] 195.0833
> mean(type2)
[1] 191.5
>
> #To calculate sample variances:
>
> var(type1)
[1] 106.0833
> var(type2)
[1] 101.3636
>
Let H0: deflection temperature under load for type1 pipe exceeds that of type2 pipe.
i.e mu1>mu2

> t.test(type1,type2)

   Welch Two Sample t-test

data: type1 and type2
t = 0.86184, df = 21.989, p-value = 0.3981
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-5.039662 12.206328
sample estimates:
mean of x mean of y
195.0833 191.5000

Since the p value(0.3981) > sig, level(0.05)

Hennce we fail to reject the null hypothesis.