b)
Z =
= 0.2309
Pvalue = Pr (Z < 0.23) = 0.4090
Assuming a significance level of 0.05, 0.4090 > alpha, therefore we do not have significant
evidence to show that the cracking rate has decreased from 25%. The sample data are compatible
with the cracking rate of 25%.
Z =
= 4.0166
Pvalue = Pr (Z < 4.016) = 0.0000
Assuming a significance level of 0.05, 0.0000 < alpha, there is evidence to say that the cracking
rate is no longer 25%. The evidence shows that the changes made to the casting process may
have helped reduce the cracking rate.
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View Full Documentc) The two hypothesis tests had different outcomes. There was not enough evidence to reject the
null hypothesis in the first test, but we rejected it in the second. The lesson to be learned is that
the pvalue decreases as the sample size increases, meaning that our tests will be more
statistically significant.
d) Yes, the results would be the same, because the zstat will just be positive instead of the
negative value that we obtained from the first test with the same pvalue.
Question 4 – Jeopardy! winnings
a) The sampling distribution of the mean winnings (in $) is bimodal with two peaks, somewhat
symmetrical, and has an outlier (at the point $35,201).
Mean = $18,459.25
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 Winter '10
 E.Fowler
 Statistics, Null hypothesis, Statistical hypothesis testing, Statistical significance, Statistical power, Ken Jennings

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