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- full-time jobs. A random sample of 81 students shows that 39 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. O Ho: Il = 0.35; Hi: < 0.35 Ho: l = 0.35; H1: Il > 0.35 Họ: 4 = 0.35; Hi: H + 0.35 Ho: P = 0.35; M1: p > 0.35 0 Hg: p = 0.35; H: p < 0.35 0 Hz: P = 0.35; Hi: p + 0.35 (b) What sampling distribution will you use? What assumptions are you making? The Student's C, since np > 5 and ng > 5. The standard normal, since np > 5 and ng > 5. The Student's t, since np < 5 and nq < 5. The standard normal, since np < 5 and ng < 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 > 0.250 0.125 < P-value < 0.250 0.050 < P-value < 0.125 0.025 < P-value < 0.050 0.005 < P-value < 0.025

Answer 1

The statistical software output for this problem is:

One sample proportion summary hypothesis test: P: Proportion of successes Ho: P = 0.35 HA: p > 0.35 Hypothesis test results: Proportion Count Total Sample Prop. Std. Err. Z-Stat P-value 39 81 0.48148148 0.052996622 2.4809408 0.0066

Hence,

What we are testing? Single Proportion

a) Level of significance = 0.05

Hypotheses: Option D is correct.

b) Sampling distribution: Option B is correct.

Test statistic = 2.48

c) 0.005 < P - value < 0.025