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Name: Professor Jennings claims that only 35% of the students at Flora Colle
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Description: 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 sho

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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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 40 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 proportionsingle mean

(a) What is the level of significance?

State the null and alternate hypotheses.

H₀: μ = 0.35; H₁: μ < 0.35

H₀: μ = 0.35; H₁: μ > 0.35

H₀: p = 0.35; H₁: p > 0.35

H₀: μ = 0.35; H₁: μ ≠ 0.35

H₀: p = 0.35; H₁: p ≠ 0.35

H₀: p = 0.35; H₁: p < 0.35

(b) What sampling distribution 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 nq < 5.

The standard normal, since np < 5 and nq < 5.

What is the value of the sample test statistic? (Round your answer to two decimal places.)

(c) Find (or estimate) the P-value.

P-value > 0.2500.

125 < P-value < 0.250

0.050 < P-value < 0.125

0.025 < P-value < 0.050

0.005 < P-value < 0.025

P-value < 0.005

Sketch the sampling distribution and show the area corresponding to the P-value.

(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 α?

At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.

At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.

At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

At the α = 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.

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