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A recent study of debt among college graduates reported that the average debt accumulated by graduates of private colleges was $38,200, with a sample standard deviation of $2,054, while the average debt accumulated by graduates of public colleges was $11,700, with a sample standard deviation of $2,075. The sample sizes were 70 and 180, respectively. Complete parts a and b below. Conduct a hypothesis test to determine if the average college debt for bachelor of arts degree recipients is at least $21,000 more for graduates from private colleges than from public colleges. Use a significance level of a = 0.025. a. Let x, = $38,200 and x2 = $11,700. State the null and alternative hypotheses. O A. Ho: H1-H> $21,000 HA H1-H25$21,000 O B. Ho H1- H2s $21,000 HA H1- H2> $21,000 OC. Ho: H1- H2< $21,000 HA H1- 422 $21,000 O D. Ho H1-H2 = $21,000 HA H1- 42 $21,000 O E. Ho: H1-H22 $21,000 HA 1- H2< $21,000 OF. Ho: H1- H2# $21,000 HA: H1-H2 = $21,000 b. Calculate the test statistic. The test statistic is | (Round to two decimal places as needed.) c. Calculate the p-value. The p-value is

A recent study of debt among college graduates reported that the average debt accumulated by graduates of private colleges was $38,200, with a sample standard deviation of $2,054, while the average debt accumulated by graduates of public colleges was $11,700, with a sample standard deviation of $2,075. The sample sizes were 70 and 180, respectively. Complete parts a and b below. Conduct a hypothesis test to determine if the average college debt for bachelor of arts degree recipients is at least $21,000 more for graduates from private colleges than from public colleges. Use a significance level of a = 0.025. a. Let x, = $38,200 and x2 = $11,700. State the null and alternative hypotheses. O A. Ho: H1-H> $21,000 HA H1-H25$21,000 O B. Ho H1- H2s $21,000 HA H1- H2> $21,000 OC. Ho: H1- H2< $21,000 HA H1- 422 $21,000 O D. Ho H1-H2 = $21,000 HA H1- 42 $21,000 O E. Ho: H1-H22 $21,000 HA 1- H2< $21,000 OF. Ho: H1- H2# $21,000 HA: H1-H2 = $21,000 b. Calculate the test statistic. The test statistic is | (Round to two decimal places as needed.) c. Calculate the p-value. The p-value is

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.5: Comparing Sets Of Data
Problem 1GP
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A recent study of debt among college graduates reported that the average debt accumulated by graduates of private colleges was$38,200​, with a sample standard deviation of​$2,054​, while the average debt accumulated by graduates of public colleges was$11,700​, with a sample standard deviation of​$2,075.The sample sizes were70and180​, respectively. Complete parts a and b below.

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A recent study of debt among college graduates reported that the average debt accumulated by graduates of private colleges was $38,200, with a sample standard deviation of $2,054, while the average debt accumulated by graduates of public colleges was $11,700, with a sample standard deviation of $2,075. The sample sizes were 70 and 180, respectively. Complete parts a and b below. Conduct a hypothesis test to determine if the average college debt for bachelor of arts degree recipients is at least $21,000 more for graduates from private colleges than from public colleges. Use a significance level of a = 0.025. a. Let x, = $38,200 and x, = $11,700. State the null and alternative hypotheses. O B. Ho: H1 - H2s $21,000 HA: 41-H2 > $21,000 O A. Ho: H1 -H2 > $21,000 HA: H1- H2s $21,000 O C. Ho: H1-H2 < $21,000 HA: H1- H22 $21,000 O D. Ho: H1-H2 = $21,000 HA: H1- H2# $21,000 O E. Ho: H1-H2 2 $21,000 HA: 41- H2< $21,000 O F. Ho: H1- H2# $21,000 HA: H1-H2 = $21,000 b. Calculate the test statistic. The test statistic is. (Round to two decimal places as needed.) c. Calculate the p-value. The p-value is
Transcribed Image Text:A recent study of debt among college graduates reported that the average debt accumulated by graduates of private colleges was $38,200, with a sample standard deviation of $2,054, while the average debt accumulated by graduates of public colleges was $11,700, with a sample standard deviation of $2,075. The sample sizes were 70 and 180, respectively. Complete parts a and b below. Conduct a hypothesis test to determine if the average college debt for bachelor of arts degree recipients is at least $21,000 more for graduates from private colleges than from public colleges. Use a significance level of a = 0.025. a. Let x, = $38,200 and x, = $11,700. State the null and alternative hypotheses. O B. Ho: H1 - H2s $21,000 HA: 41-H2 > $21,000 O A. Ho: H1 -H2 > $21,000 HA: H1- H2s $21,000 O C. Ho: H1-H2 < $21,000 HA: H1- H22 $21,000 O D. Ho: H1-H2 = $21,000 HA: H1- H2# $21,000 O E. Ho: H1-H2 2 $21,000 HA: 41- H2< $21,000 O F. Ho: H1- H2# $21,000 HA: H1-H2 = $21,000 b. Calculate the test statistic. The test statistic is. (Round to two decimal places as needed.) c. Calculate the p-value. The p-value is
d. State the conclusion for this hypothesis test. O A. Do not reject Ho. There is sufficient evidence at the a= 0.025 level of significance to conclude that graduates of private colleges have at least $21,000 more in college-related debt. B. Reject Ho. There is not sufficient evidence at the a = 0.025 level of significance to conclude that graduates of private colleges have at least $21,000 more in college-related debt. OC. Reject Ho- There is sufficient evidence at the a = 0.025 level of significance to conclude that graduates of private colleges have at least $21,000 more in college-related debt. D. Do not reject Ho. There is not sufficient evidence at the a = 0.025 level of significance to conclude that graduates of private colleges have at least $21,000 more in college-related debt.
Transcribed Image Text:d. State the conclusion for this hypothesis test. O A. Do not reject Ho. There is sufficient evidence at the a= 0.025 level of significance to conclude that graduates of private colleges have at least $21,000 more in college-related debt. B. Reject Ho. There is not sufficient evidence at the a = 0.025 level of significance to conclude that graduates of private colleges have at least $21,000 more in college-related debt. OC. Reject Ho- There is sufficient evidence at the a = 0.025 level of significance to conclude that graduates of private colleges have at least $21,000 more in college-related debt. D. Do not reject Ho. There is not sufficient evidence at the a = 0.025 level of significance to conclude that graduates of private colleges have at least $21,000 more in college-related debt.
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