A college claims that the proportion, p, of students who commute more than fifteen miles to school is less than 25%. A researcher wants to test this. A random sample of 260 students at this college is selected, and it is found that 47 commute more than fifteen miles to school. Is there enough evidence to support the college's claim at the 0.10 level of significance? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis H and the alternative hypothesis H₁. (b) Determine the type of test statistic to use. (Choose one) ▼ (c) Find the value of the test statistic. (Round to three or more decimal places.) 0 (d) Find the p-value. (Round to three or more decimal places.) (e) Is there enough evidence to support the claim that the proportion of students who commute more than fifteen miles to school is less than 25%? OYes O No = Ix b ☐☐ $ $ 0.6 P 0=0 OSO 020 ☐☐ 010 ロ<ロ
A college claims that the proportion, p, of students who commute more than fifteen miles to school is less than 25%. A researcher wants to test this. A random sample of 260 students at this college is selected, and it is found that 47 commute more than fifteen miles to school. Is there enough evidence to support the college's claim at the 0.10 level of significance? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis H and the alternative hypothesis H₁. (b) Determine the type of test statistic to use. (Choose one) ▼ (c) Find the value of the test statistic. (Round to three or more decimal places.) 0 (d) Find the p-value. (Round to three or more decimal places.) (e) Is there enough evidence to support the claim that the proportion of students who commute more than fifteen miles to school is less than 25%? OYes O No = Ix b ☐☐ $ $ 0.6 P 0=0 OSO 020 ☐☐ 010 ロ<ロ
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![A college claims that the proportion, \( p \), of students who commute more than fifteen miles to school is less than 25%. A researcher wants to test this. A random sample of 260 students at this college is selected, and it is found that 47 commute more than fifteen miles to school. Is there enough evidence to support the college’s claim at the 0.10 level of significance?
Perform a one-tailed test. Then complete the parts below:
Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.)
(a) State the null hypothesis \( H_0 \) and the alternative hypothesis \( H_1 \).
- \( H_0: \) [ ]
- \( H_1: \) [ ]
(b) Determine the type of test statistic to use.
- (Choose one) ▼
(c) Find the value of the test statistic. (Round to three or more decimal places.)
- [ ]
(d) Find the p-value. (Round to three or more decimal places.)
- [ ]
(e) Is there enough evidence to support the claim that the proportion of students who commute more than fifteen miles to school is less than 25%?
- ☐ Yes ☐ No
**Diagram Explanation:**
On the right side, there is a chart with symbols representing statistical parameters and their corresponding notations:
- \(\mu, \sigma, p\): Population mean, standard deviation, and proportion
- \(X, \bar{x}, s\): Sample mean and standard deviation
- Various symbols for statistical calculations, possibly including notations for variance, correlation, etc.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F695b3528-6039-4e40-a953-e41012406323%2F47a63abc-e525-4814-bd71-ea967ff0bcd3%2Fyalcknj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A college claims that the proportion, \( p \), of students who commute more than fifteen miles to school is less than 25%. A researcher wants to test this. A random sample of 260 students at this college is selected, and it is found that 47 commute more than fifteen miles to school. Is there enough evidence to support the college’s claim at the 0.10 level of significance?
Perform a one-tailed test. Then complete the parts below:
Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.)
(a) State the null hypothesis \( H_0 \) and the alternative hypothesis \( H_1 \).
- \( H_0: \) [ ]
- \( H_1: \) [ ]
(b) Determine the type of test statistic to use.
- (Choose one) ▼
(c) Find the value of the test statistic. (Round to three or more decimal places.)
- [ ]
(d) Find the p-value. (Round to three or more decimal places.)
- [ ]
(e) Is there enough evidence to support the claim that the proportion of students who commute more than fifteen miles to school is less than 25%?
- ☐ Yes ☐ No
**Diagram Explanation:**
On the right side, there is a chart with symbols representing statistical parameters and their corresponding notations:
- \(\mu, \sigma, p\): Population mean, standard deviation, and proportion
- \(X, \bar{x}, s\): Sample mean and standard deviation
- Various symbols for statistical calculations, possibly including notations for variance, correlation, etc.
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