**Hypothesis Testing for Proportion of Students with Jobs at Flora College**Professor Jennings claims that only 35% of the students at Flora College work while attending school. Dean Renata thinks that the professor has underestimated the number of students with part-time or full-time jobs. A random sample of 84 students shows that 37 have jobs. Do the data indicate that more than 35% of the students have jobs? Use a 5% level of significance.### What are we testing in this problem?- Single Proportion- Single Mean### (a) What is the level of significance?- [input box]### State the null and alternate hypotheses.- $ H_{0}: p = 0.35; \ H_{1}: p \neq 0.35 $- $ H_{0}: \mu = 0.35; \ H_{1}: \mu < 0.35 $- $ H_{0}: p = 0.35; \ H_{1}: p > 0.35 $- $ H_{0}: \mu = 0.35; \ H_{1}: \mu > 0.35 $- $ H_{0}: \mu = 0.35; \ H_{1}: \mu \neq 0.35 $- $ H_{0}: p = 0.35; \ H_{1}: p < 0.35 $### (b) What sampling distribution will you use? What assumptions are you making?- The standard normal, since $ np > 5 $ and $ nq > 5 $.- The Student's t, since $ np < 5 $ and $ nq < 5 $.- The standard normal, since $ np < 5 $ and $ nq < 5 $.- The Student's t, since $ np > 5 $ and $ nq > 5 $.### What is the value of the sample test statistic? (Round your answer to two decimal places.)- [input box]### (c) Find the P-value. (Round your answer to four decimal places.)- [input box] ### P-Values and Hypothesis Testing#### Sketch the sampling distribution and show the area corresponding to the P-value.In the provided graphs, the sampling distributions are illustrated as normal distributions (bell curves). The shaded areas under these curves represent the P-values corresponding to different hypothesis tests.1. **Graph 1**: The shaded area is on the left side under the curve, starting from $ -3 $ to approximately $ -1.5 $.2. **Graph 2**: The shaded area is on the right side under the curve, starting from approximately $ 1 $ to $ 3 $.3. **Graph 3**: The shaded areas are on both tails of the curve, starting from $ -3 $ to approximately $ -1.5 $ and approximately $ 1.5 $ to $ 3 $.4. **Graph 4**: The shaded area is on the right side under the curve, starting from approximately $ 2 $ to $ 3 $.#### Multiple-Choice Questions:**(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level $\alpha$?**- ○ At the $\alpha = 0.05$ level, we reject the null hypothesis and conclude the data are statistically significant.- ○ At the $\alpha = 0.05$ level, we reject the null hypothesis and conclude the data are not statistically significant.- ○ At the $\alpha = 0.05$ level, we fail to reject the null hypothesis and conclude the data are statistically significant.- ○ At the $\alpha = 0.05$ level, we fail to reject the null hypothesis and conclude the data are not statistically significant.**(e) Interpret your conclusion in the context of the application.**- ○ There is sufficient evidence at the 0.05 level to conclude that more than 35% of the students have jobs.- ○ There is insufficient evidence at the 0.05 level to conclude that more than 35% of the students have jobs.### Explanation of the Graphs:- **Graph 1**: Represents a one-tailed test where the critical region is on the left end. If the test statistic falls within this region, the null hypothesis would be rejected.- **Graph 2

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Description: **Hypothesis Testing for Proportion of Students with Jobs at Flora College**Professor Jennings claims that only 35% of the students at Flora College work while attending school. Dean Renata thinks that the professor has underestimated the number of

It is given that the random samples of 84 students, 37 students have jobs.

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Statistics

Professor Jennings claims that only 35% of the students at Flora College work while attending school. Dean Renata thinks that the professor has underestimated the number of students with part-time or full-time jobs. A random sample of 84 students shows that 37 have jobs. Do the data indicate that more than 35% of the students have jobs? Use a 5% level of significance. What are we testing in this problem? single proportion single mean (a) What is the level of significance? State the null and alternate hypotheses. Ho: p = 0.35; H1: p + 0.35 Ho: H = 0.35; H1: µ < 0.35 %3D Но: р %3D 0.35; Hi: р> 0.35 Ho: H = 0.35; H1: µ > 0.35 %3D Ho: H = 0.35; H1: µ ± 0.35 %3D Но: р %3D 0.35; Hi: р < 0.35 (b) What sampling distr The standard normal, since np > 5 and nq > 5. ution will you use? What assumptions are you making? The Student's t, since np < 5 and nq < 5. The standard normal, since np < 5 and nq < 5. The Student's t, since np > 5 and ng > 5. What is the value of the sample test statistic? (Round your answer to two decimal places.) (c) Find the P-value. (Round your answer to four decimal places.)

Professor Jennings claims that only 35% of the students at Flora College work while attending school. Dean Renata thinks that the professor has underestimated the number of students with part-time or full-time jobs. A random sample of 84 students shows that 37 have jobs. Do the data indicate that more than 35% of the students have jobs? Use a 5% level of significance. What are we testing in this problem? single proportion single mean (a) What is the level of significance? State the null and alternate hypotheses. Ho: p = 0.35; H1: p + 0.35 Ho: H = 0.35; H1: µ < 0.35 %3D Но: р %3D 0.35; Hi: р> 0.35 Ho: H = 0.35; H1: µ > 0.35 %3D Ho: H = 0.35; H1: µ ± 0.35 %3D Но: р %3D 0.35; Hi: р < 0.35 (b) What sampling distr The standard normal, since np > 5 and nq > 5. ution will you use? What assumptions are you making? The Student's t, since np < 5 and nq < 5. The standard normal, since np < 5 and nq < 5. The Student's t, since np > 5 and ng > 5. What is the value of the sample test statistic? (Round your answer to two decimal places.) (c) Find the P-value. (Round your answer to four decimal places.)

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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