Question

An education rehearser claims that at most 5% of working college students are employed as teachers or teaching assistants. In a random sample of 250 working college students, 15 of them are employed as teachers or teaching assistants. Is there enough evidence to support your thinking at α = 0.05?

1. The proportion of students in the sample who are employed as teachers or teaching assistants is

2. Null hypothesis p̂ > 0.06 μ = 0.06 p̂ = 0.05 p > 0.05 p̂ = 0.06 p̂ < 0.06 p = 0.06 p = 0.05 p < 0.05

3. Alternative hypothesis p < 0.05 μ = 0.06 p̂ < 0.06 p > 0.05 p̂ = 0.06 p = 0.06 p̂ > 0.06 p = 0.05 p̂ = 0.05

4. Is Success/Failure condition met? Yes No No enough information

5. Observed test statistic

6. P-value ”use 4 decimals”

7. Is there evidence to support the claim at 5% significance level?

Answer 1

1)

The proportion of students in the sample who are employed as teachers or teaching assistants is = 0.06

2)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.05

3)
Alternative Hypothesis, Ha: p > 0.05

4)

yes

5)

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.06 - 0.05)/sqrt(0.05*(1-0.05)/250)
z = 0.73

6)

P-value Approach
P-value = 0.2327

7)

As P-value >= 0.05, fail to reject null hypothesis.
There is not sufficient evidence to support the claim