Question

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 82 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.

(a) State the null and alternate hypotheses. Options:

H₀: μ = 0.35; H₁: μ < 0.35

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: 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? Options:

The standard normal, 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 Student's t, since np < 5 and nq < 5.

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

(d) Find (or estimate) the P-value. Options:

P-value > 0.250

0.125 < 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

(e) 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? Options:

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.

Answer 1

The statistical software output for this problem is :

(a)

Level of significance = 0.05

Option F is correct .

(b)

Option B is correct.

(c) Test statistics = 1.92

0.025 < P-value < 0.050

(d)

Graph is correct

(d)Option is correct.

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