For the problem of testing hypotheses for the means arising from two populations, we will be using the functions `z.test`

and `t.test`

.

- As earlier, load the
`library(PASWR)`

library. - Carry out the Z-test using
`z.test`

and the options`x`

,`y`

,`sigma.x`

, and`sigma.y`

:The p-value is very small (pH_Data <- c(8.30, 8.42, 8.44, 8.32, 8.43, 8.41, 8.42, 8.46, 8.37, 8.42) pH_New <- c(8.78, 8.85, 8.74, 8.83, 8.82, 8.79, 8.82, 8.74, 8.84, 8.78, 8.75, 8.81) z.test(x=pH_Data,y=pH_New,sigma.x=sigma.y=0.05,alternative="less")

`2.2e-16`

) indicating that we reject the null hypothesis that . - For the steel length cut data problem, run ...

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