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ILLINOIS CENTRAL COLLEGE MATH 225 STATISTICS GRADED PASS
- Course
- MATH 225
- Institution
- Illinois Central College
ILLINOIS CENTRAL COLLEGE MATH 225 STATISTICS GRADED PASS
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ILLINOIS CENTRAL COLLEGE MATH 225 STATISTICSGRADED PASS
14. A mechanic wants to show that more than 44% of car owners do not follow a normal maintenance
schedule. Identify the null hypothesis, H0, and the alternative hypothesis, Ha, in terms of the parameter
p.
H0: p≤0.44; Ha: p>0.44
Let the parameter p be used to represent the proportion.
Remember that the null hypothesis is the statement already believed to be true and the alternative
hypothesis is the statement that is trying to be shown. In this case, the mechanic is trying to show that
more than 44% of people do not follow the maintenance schedule. So the alternative hypothesis is
p>0.44. The null hypothesis is the opposite of this: p≤0.44.
Also, remember that the null hypothesis is always stated with some form of equality: equal (=), greater
than or equal to (≥), or less than or equal to (≤). So we can double check that our answer above makes
sense.
15. Suppose the null hypothesis, H0, is: a weightlifting bar can withstand weights of 800 pounds and
less. What is α, the probability of a Type I error in this scenario?
the probability that you think the weightlifting bar cannot withstand weights of 800 pounds and less
when, in fact, it can
A Type I error is the decision to reject the null hypothesis when it is true. In this case, the Type I error is
thinking that the bar cannot withstand weights of 800 pounds and less when, in fact, it can.
16. Suppose the null hypothesis, H0, is: the mean age of the horses on a ranch is 6 years. What is the
Type II error in this scenario?
You think the mean age of the horses on a ranch is 6 years when, in fact, it is not.
A Type II error is the decision not to reject the null hypothesis when, in fact, it is false. In this case, the
Type II error is thinking that the mean age of the horses is 6 years when, in fact, it is not.
Type I and Type II Errors
When you perform a hypothesis test, there are four possible outcomes depending on the actual truth (or
falseness) of the null hypothesis, H0, and the decision to reject the null hypothesis or not. Two of the
, decisions are the correct outcomes but, since statistics cannot prove anything with certainty, there will
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