Automobiles Purchased An automobile owner found that 20 years ago, 72% of Americans said that they would prefer to purchase an American automobile. He believes that the number differs from 72% today. He selected a random sample of 43 Americans and found that 38 said that they would prefer an American automobile. Can it be concluded that the percentage today differs from 72%? At a =0.10, is he correct? Use the critical value method with tables. Do not round intermediate steps. Part: 0 / 5 Part 1 of 5 (a) State the hypotheses and identify the claim. Ho : (Choose one) ▼ H : (Choose one) ▼ This hypothesis test is a (Choose one) ▼ test.

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The first pic is the question, since I’ve been receiving some incorrect answers from the tutors, I included an example problem in the second pic
Automobiles Purchased An automobile owner found that 20 years ago, 72% of Americans said that they would prefer
to purchase an American automobile. He believes that the number differs from 72% today. He selected a random sample
of 43 Americans and found that 38 said that they would prefer an American automobile. Can it be concluded that the
percentage today differs from 72%? At a = 0.10, is he correct? Use the critical value method with tables. Do not round
intermediate steps.
Part: 0 / 5
Part 1 of 5
(a) State the hypotheses and identify the claim.
Ho :
(Choose one) ▼
H :
(Choose one) ▼
This hypothesis test is a (Choose one) ▼ test.
Transcribed Image Text:Automobiles Purchased An automobile owner found that 20 years ago, 72% of Americans said that they would prefer to purchase an American automobile. He believes that the number differs from 72% today. He selected a random sample of 43 Americans and found that 38 said that they would prefer an American automobile. Can it be concluded that the percentage today differs from 72%? At a = 0.10, is he correct? Use the critical value method with tables. Do not round intermediate steps. Part: 0 / 5 Part 1 of 5 (a) State the hypotheses and identify the claim. Ho : (Choose one) ▼ H : (Choose one) ▼ This hypothesis test is a (Choose one) ▼ test.
Sample Question
Automobiles Purchased An automobile owner found that 20 years ago, 75% of Americans said that they would
prefer to purchase an American automobile. He believes that the number is much greater than 75% today. He
selected a random sample of 54 Americans and found that 43 said that they would prefer an American automobile.
Can it be concluded that the percentage today is greater than 75%? At a=0.01, is he correct? Use the critical value
method with tables. Do not round intermediate steps.
(a) State the hypotheses and identify the claim.
(b) Find the critical value(s).
(c) Compute the test value.
(d) Make the decision.
(e) Summarize the results.
Explanation
(a) State the hypotheses and identify the claim.
The null hypothesis H, is the statement that there is no difference between a parameter and a specific value. This is
equivalent to Ho:p=0.75.
The alternative hypothesis H, is the statement that there is a difference between a parameter and a specific value.
In this case, the percentage of Americans who said that they would prefer to purchase an American automobile is
greater than 75%. This is equivalent to H :p>0.75.
The problem asks, "Can it be concluded that the percentage of Americans who said that they would prefer to
purchase an American automobile is greater than 75%?"
Hence, the claim is the alternative hypothesis.
(b) Find the critical value(s).
From the figure below, for a right-tailed test with a- 0.01, the critical value is z-+2.33.
a=0.10, C.V.- +1.28
Ho:p=k
a=0.05, C.V.=+1.65
H:p>k
a-0.01, C.V.-+2.33
(c) Compute the test value.
Formula for the : Test for Proportions
Vpgln
A X
where p == sample proportion
p- population proportion
q=1-p
n- sample size
First, it is necessary to find p. p, and q.
43
54
-0.796
P- 75%
-0.75
9 =1-p
=1-0.75
= 0.25
Using the formula for the z-test for proportions, compute the test value.
Vpg'n
0.796 -0.75
V(0.75)(0.25)/54
= 0.78
Transcribed Image Text:Sample Question Automobiles Purchased An automobile owner found that 20 years ago, 75% of Americans said that they would prefer to purchase an American automobile. He believes that the number is much greater than 75% today. He selected a random sample of 54 Americans and found that 43 said that they would prefer an American automobile. Can it be concluded that the percentage today is greater than 75%? At a=0.01, is he correct? Use the critical value method with tables. Do not round intermediate steps. (a) State the hypotheses and identify the claim. (b) Find the critical value(s). (c) Compute the test value. (d) Make the decision. (e) Summarize the results. Explanation (a) State the hypotheses and identify the claim. The null hypothesis H, is the statement that there is no difference between a parameter and a specific value. This is equivalent to Ho:p=0.75. The alternative hypothesis H, is the statement that there is a difference between a parameter and a specific value. In this case, the percentage of Americans who said that they would prefer to purchase an American automobile is greater than 75%. This is equivalent to H :p>0.75. The problem asks, "Can it be concluded that the percentage of Americans who said that they would prefer to purchase an American automobile is greater than 75%?" Hence, the claim is the alternative hypothesis. (b) Find the critical value(s). From the figure below, for a right-tailed test with a- 0.01, the critical value is z-+2.33. a=0.10, C.V.- +1.28 Ho:p=k a=0.05, C.V.=+1.65 H:p>k a-0.01, C.V.-+2.33 (c) Compute the test value. Formula for the : Test for Proportions Vpgln A X where p == sample proportion p- population proportion q=1-p n- sample size First, it is necessary to find p. p, and q. 43 54 -0.796 P- 75% -0.75 9 =1-p =1-0.75 = 0.25 Using the formula for the z-test for proportions, compute the test value. Vpg'n 0.796 -0.75 V(0.75)(0.25)/54 = 0.78
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