In: Statistics and Probability
Q32 The manufacturer of a quartz travel alarm clock claims that, on the average, its clocks deviate from perfect time by 30 seconds per month, with a standard deviation of 10 seconds. Engineers from a consumer magazine purchase 40 of the clocks and find that the average clock in the sample deviated from perfect accuracy by 34 seconds in one month. [4 Marks]
(a) If the manufacturer’s claim is correct (i.e., seconds, seconds), what is the probability that the average deviation from perfect accuracy would be 34 seconds or more?
(b) Based on your answer to part (a), speculate on the possibility that the manufacturer’s claim might not be correct.
DO NOT WRITE THE ANSWERS - USE WORD FORMAT.
Let X denote the deviation (in seconds) of a quartz travel alarm clock per month
Now, we are given that:
Now, the engineers took a sample of size n = 40 (can be considered large), thus the distribution of the sample average cam be approximated as:
, the standard normal distribution.
(a)
The required probability is given by:
(b)
From part (a) we observe that the probability of observing the outcome as extreme as we have observed (a sample of 40 clocks on average deviates from perfect accuracy by 34 seconds on average in one month) is very less (0.005706). Thus, if the watchmaker's claim is right, then the probability of that happening by chance is very less and thus, we can conclude that the manufacturer's claim is wrong.
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