Question

per gallo 13. FILE A new assembly-line procedure to increase production has been suggested. To test whether the new procedure is superior to the old procedure, a random sam- ple of 15 assembly-line workers was selected. The number of units produced in an hour under the old procedure was determined, then the new procedure was

Answer 1

This is an example of paired t-test

Ho :The new assembly procedure is not effective in increasing the production VS H1 :The new assembly procedure is effective in increasing the production Ho: Mid = 0 vs H1 : Jld > 0 where ud is the population mean of the random variable d = Xnew – Xald

The calculations regarding the statistical test are shown below:

> n <- > x_old <- c(60,40,59,30,70,78,43,40,87,58,56,21,99,50,56) > x_new <- c(64,52,58,37,71,83,46,52,84,80,57,21,108,56,62) > d <- x new - x_old; > d_bar <- mean(d) > 5_d <- sd(d) ## the standard deviation of d length(d) > # The test statistic is > to <- (d_bar - 0)/(s_d/sqrt(n));t0 [1] 3.412267 > # Critical value is > alpha <- 0.05 >t.critical <- qt(alpha, df = n-1, lower.tail = FALSE);t.critical [1] 1.76131

(b) Decision rule: Reject H0 at 5% l.o.s if test statistic t0 > 1.7613.

(c)

As the test statistic = 3.4123 > 1.7613, we can reject H0 at 5% l.o.s. Hence, the new assembly procedure is effective in increasing the production.

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