4. A lab technician plans to c
4. A lab technician plans to check the calibration of anelectronic scale by repeatedly weighing the same 10-kg specimen andobserving each reading. The scale won’t give the exact samemeasurement with each weighing due to inherent variability in thereadings; assume that the standard deviation of the readings has astandard deviation of σ = 0.1 kg.
(a) State the null and alternative hypotheses that would be usedin a hypothesis test for this situation; state them usingmathematical notation (H0 and Ha) as well as by giving a verbaldescription of each hypothesis
(b) What action will be taken if the decision of the test is toreject H0?
(c) It is desired to construct a 95% confidence interval for themean reading from the scale (when a 10-kg specimen is placed onit). The goal is to have a margin of error no greater than±0.05,kg. What is the smallest number of readings that should betaken 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 samplemean of the readings is observed to be x¯ = 9.983 kg. Calculate the95% confidence interval on the population mean of the readings.
(e) Based off of your confidence interval calculated above, whatis 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 havebeen made with this decision?[2]
Answer:
(a)
Hypotheses are:
H0: The true average measurements is equal to 10.
H1: The true average measurements is not equal to10.
(b)
If the decision of the test is to reject H0 then lab technicianshould plan to calibrate the electronic scale.
(C)
(d)
(e)
Since confidence interval contains 10 so we fail to reject thenull hypothesis on the basis of confidence interval.
Since we fail to reject the null hypothesis so type II error ispossible.
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