Question

Prudent Furniture Company manufactures office furniture and other office equipment at several plants in southern China. Over the last few years, the ergonomic office chair was produced in the Panyu plant. The dailly production rate of the office chair was known to follow a normal distribution with a mean number of 20 and a standard deviation of 1.6. Since last year, the production of the office chair has been shifted to the Shenzhen plant. The production manager of the company would like to know whether the average daily production rate of the office chair has changed or not since the shift. Accordingly, a random sample of 50 working days was selected and the mean number of office chairs produced was found to be 19.6. a Perform an appropriate hypothesis test to determine whether the mean number of the office chair produced daily has changed or not at the 0.01 level of significance. b Use the p-value approach to test the above hypothesis at the same level of significance. c With regard to the result of the above hypothesis testing, which type of error (type I or type II) could possibly be comitted? Explain briefly.

Answer 1

(a)

Null Hypothesis : H₀ : = 20

Alternative hypothesis : H_a : 20

standard deviation = = 1.6

standard error of sampling distribution = /sqrt(n) = 1.6/sqrt(50) = 0.2263 per day

Test statistic

Z = (19.6 - 20)/0.2263 = -1.7676

Here critical value of Z for 0.01 level of significance

Z_critical = +- 2.576

so here

Z < Z_critical so we will fail to reject the null hypothesis.

(b) Here

p - value = 2 * Pr(Z > 1.7676) = 2 * 0.0386 = 0.0771

Here p -value is greater than 0.01 so we would fail to reject the null hypothesis.

(c) Here as we failed to reject the null hypothesis, we could possbily be committing type II error.