21. On a test of motor coordination, the population of average bowlers has a mea

Question

21. On a test of motor coordination, the population of average bowlers has a mean score of 24, with a standard deviation of 6. A random sample of 30 bowlers at Bubba's Bowling Alley has a sample mean of 26. A second random sample of 30 bowl- ers, at Babette's Bowling Alley, has a mean of 18 Using the .05 criterion and both tails of the sam pling distribution, decide if each sample represents the population of average bowlers. 22 (a) In question 21, if a particular sample does not represent the population of average bowlers, what is your best estimate of the population u it does rep- resent? (b) Explain the logic behind this conclusion. 23. A couple with eight daughters docide

Explanation / Answer

a)

If a particular sample does not represent the population of the average bowlers

and if we do not know the population average

our best estimate comes from the central limit theorem that

Mean of sample=population mean  

Now according to question 21 we already know the population average as 24

So if the mean of the sample is 18 then we can conclude that there are outliers in the data points

ie there are a few bowlers who have very weak motor coordination hence the average is so low  

b)

The logic behind the conclusion is :

Lets say on a average the bowlers scores are 23,22,24,26

Lets say there are other sets of bowlers whose score are 16,17,19

The average of the first group is 24 but the average of second group is 18

Hence we can say that the seond group is an outlier group in comparision to the population of bowlers

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