Question

Traditionally 18% of undergraduates in the U.S. major in business. A recent sample of 863 undergraduates found 21% major in business. Perform a hypothesis test to see if the percentage of undergraduates majoring in business has significantly increased from past norms

A. What is H_{o} ?

B. What is H_{1}?

C. Assuming α = 2.5%, what is the test statistic for this hypothesis test?

D. Assuming α = 2.5%, what is the critical value for this hypothesis test?

E. What is the conclusion to this hypothesis test for α = 2.5%?

F. Assuming α = 1%, what would be the conclusion to this hypothesis test?

Answer #1

Below are the null and alternative Hypothesis,

a)

Null Hypothesis, H0: p = 0.18

b)

Alternative Hypothesis, Ha: p > 0.18

c)

Test statistic,

z = (pcap - p)/sqrt(p*(1-p)/n)

z = (0.21 - 0.18)/sqrt(0.18*(1-0.18)/863)

z = 2.29

d)

Rejection Region

This is right tailed test, for α = 0.025

Critical value of z is 1.96.

Hence reject H0 if z > 1.96

e)

reject the null hypothesis.

f)

This is right tailed test, for α = 0.01

Critical value of z is 2.33.

Hence reject H0 if z > 2.33

fail to reject the null hypothesis.

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sample of 411 households from a community in Montana are shown
below.
Type of Household
Percent of U.S.
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Observed Number
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Married with children
26%
96
Married, no children
29%
113
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97
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distribution of U.S. households fits the...

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sample of 411 households from a community in Montana are shown
below.
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Percent of U.S.
Households
Observed Number
of Households in
the Community
Married with children
26%
104
Married, no children
29%
112
Single parent
9%
32
One person
25%
97
Other (e.g., roommates, siblings)
11%
66
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distribution of U.S. households fits the...

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sample of 411 households from a community in Montana are shown
below.
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Percent of U.S.
Households
Observed Number
of Households in
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Married with children
26%
93
Married, no children
29%
127
Single parent
9%
35
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25%
88
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11%
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