Question

4. A lab technician plans to check the calibration of an electronic scale by repeatedly weighing the same 10-kg specimen and observing each reading. The scale won’t give the exact same measurement with each weighing due to inherent variability in the readings; assume that the standard deviation of the readings has a standard deviation of σ = 0.1 kg.

(a) State the null and alternative hypotheses that would be used in a hypothesis test for this situation; state them using mathematical notation (H0 and Ha) as well as by giving a verbal description of each hypothesis

(b) What action will be taken if the decision of the test is to reject H0?

(c) It is desired to construct a 95% confidence interval for the mean reading from the scale (when a 10-kg specimen is placed on it). The goal is to have a margin of error no greater than ±0.05,kg. What is the smallest number of readings that should be taken in order to obtain this desired bound on the margin of error? Make sure you round your answer up to the next integer.

(d) Suppose that n = 40 weighings are performed, and the sample mean of the readings is observed to be x¯ = 9.983 kg. Calculate the 95% confidence interval on the population mean of the readings.

(e) Based off of your confidence interval calculated above, what is the decision of the hypothesis test if a significance level of α = 0.05 is used? What type of error (Type I or Type II) might have been made with this decision?[2]

Answer 1

(a)

Hypotheses are:

H0: The true average measurements is equal to 10.

H1: The true average measurements is not  equal to 10.

(b)

If the decision of the test is to reject H0 then lab technician should plan to calibrate the electronic scale.

(C)

(d)

(e)

Since confidence interval contains 10 so we fail to reject the null hypothesis on the basis of confidence interval.

Since we fail to reject the null hypothesis so type II error is possible.