Only 26% of psychology majors are satisfied with their career paths as compared to 50% of accounting majors (The Wall Street Journal, October 11, 2010). Suppose these results were obtained from a survey of 300 psychology majors and 350 accounting majors. Let p1 represent the population proportion of satisfied accounting majors and p2 the population proportion of satisfied psychology majors. a. Develop the appropriate null and alternative hypotheses to test whether the proportion of accounting majors satisfied with their career paths differs from psychology majors by more than 20 percentage points. multiple choice 1 H0: p1 − p2 = 0.20; HA: p1 − p2 ≠ 0.20 H0: p1 − p2 ≤ 0.20; HA: p1 − p2 > 0.20 H0: p1 − p2 ≥ 0.20; HA: p1 − p2 < 0.20 b. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.) c. Find the p-value. multiple choice 2 p-value < 0.01 0.01 ≤ p-value < 0.025 0.025 ≤ p-value < 0.05 0.05 ≤ p-value < 0.10 p-value ≥ 0.10 d. At the 5% significance level, what is the conclusion? multiple choice 3 Reject H0; the difference in the proportions is more than 20% Reject H0; the difference in the proportions is not more than 20% Do not reject H0; the difference in the proportions is more than 20% Do not reject H0; the difference in the proportions is not more than 20%
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Only 26% of psychology majors are satisfied with their career paths as compared to 50% of accounting majors (The Wall Street Journal, October 11, 2010). Suppose these results were obtained from a survey of 300 psychology majors and 350 accounting majors.
Let p1 represent the population proportion of satisfied accounting majors and p2 the population proportion of satisfied psychology majors.
a. Develop the appropriate null and alternative hypotheses to test whether the proportion of accounting majors satisfied with their career paths differs from psychology majors by more than 20 percentage points.
multiple choice 1
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H0: p1 − p2 = 0.20; HA: p1 − p2 ≠ 0.20
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H0: p1 − p2 ≤ 0.20; HA: p1 − p2 > 0.20
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H0: p1 − p2 ≥ 0.20; HA: p1 − p2 < 0.20
b. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)
c. Find the p-value.
multiple choice 2
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p-value < 0.01
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0.01 ≤ p-value < 0.025
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0.025 ≤ p-value < 0.05
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0.05 ≤ p-value < 0.10
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p-value ≥ 0.10
d. At the 5% significance level, what is the conclusion?
multiple choice 3
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Reject H0; the difference in the proportions is more than 20%
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Reject H0; the difference in the proportions is not more than 20%
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Do not reject H0; the difference in the proportions is more than 20%
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Do not reject H0; the difference in the proportions is not more than 20%
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