AP Statistics Spring High Name EXAM: Hypothesis Test of 1 sample proportions Ans

Question

AP Statistics Spring High Name EXAM: Hypothesis Test of 1 sample proportions Answer each part as completely as possible, show all formulas using, labei all value..SHOW ALL WORK for full credit 1. To increase the Interest in baseball, MLB's commissioner's office has started a social media campaiga just before the season on facebook twitter and other social media platforms. In past polls it was estimated 30% ofAmericans favored baseball over other sports. Several months after starting thelr ad campaign the commissioner's office hired a polling firm which randomly selected 2500 American adults and asked them which sport was their favorite a. Show whether or not the conditions for inference were met for a hypothesis test b. Write the null and alternative hypothesis. CThe polling firm found a p-value of 0.0402, what concusion did they draw? d State what the p-value represents in context of the situation A drug company has developed a new test for a particular disease. The disease lowers the white cell monocyte count in the blood and the test measures this to detect a percentage of monocyte is 4% to 8% but the disease eliminates all but at most 2% (this existence of the disease in the host Typically the i, yourFe) of the monocyte assuming you are sic, looking for cell in any given host. The null hypothesis is Ha: p 02, that is this test starts off ofthe time while inaccurately detecting the disease 1% of the time. that you are not sie, K-p>02. Studies on the test have found that it wil, accurately detect the disease 995% a In context of the situation, what is a type l error? In contest of the situation, what is a type l errort c Which of the two errors is worst? ln context of the situation what does this mean? d. What is the power of this Mypothesis test and

Explanation / Answer

1)

a)

The necessary conditions for a hypothesis test are:

Since, it is given in the problem statement that the subjects were chosen randomly and N is large enough (N > 30), the conditions were met for a hypothesis test.

b)

Null and Alternate Hypothesis:

H0: Proportion of American People favouring Football = .3

H1: Proportion of American People favouring Football <> .3

c)

if alpha = 0.05

then the given p-value ie 0.0402 is less than 0.05. Hence we fail to reject the null hypothesis.

d)

The p-value represents that the proportion of American Adults favouring football is 0.3 or 30%.

2)

a)

A type I error is the incorrect rejection of the null hypothesis.

Ie a patient has been said not to have the disease when in fact he has the disease.

b)

A Type II error is the incorrect retention of the null hypothesis.

i.e A patient has been said to have the disease when in fact he does not has the disease.

c)

Depending on the scenario one can classify which of the two case is worse.

In the given example, A type II error is worst as patient is wrongly said not to have this decease when in-fact he has the disease. If the disease is fatal, the time diagnosis might have saved the life of the patient.

d)

Power of a test is the Probability of rejecting the null hypothesis given that it is not true.

In the given example, we say that the patient does not have the disease when infact he/she is sick.

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