Question

An education researcher daims that at most 7% of working college students are employed as teachers or teaching assistants. In a random sample of 300 working college students, 9% are employed as teachers or teaching assistants. At a 0.01, is there enough evidence to reject the researcher's claim? Complete parts (a) through (e) below. (a) Identify the claim and state Ho and H, Identify the claim in this scenario. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) O A. At most % of working college students are employed as teachers or teaching assistants. O B. The percentage of working college students who are employed as teachers or teaching assistants is not %. O C. More than % of working college students are employed as teachers or teaching assistants. O D. % of working college students are employed as teachers or teaching assistants. Let p be the population proportion of successes, where a success is a working college student who is employed as a teacher or teaching assistant. State H, and H, Select the correct choice below and fill in the answer boxes to complete your choice (Round to two decimal places as needed.) O A. H. ne O B. H. n n C. H. n= Click to select your answer(S)

Answer 1

From the given details where the population proportion is p= 0.07 and a sample of 300 working college students are taken for testing. The sample proportion is $\bar{p}$=0.09

So, p*n(1-p)=19.53 >10 hence we can assume it as normal distribution and satisfactory assumption for the Z test.

a) The claim is:

A. At most 7% of the working college students are employed as teachers or teaching assistants.

The Hypotheses are:

Ho:p<0.07

Ha: p > 0.07

b) At 0.01 level of significance, the critical value for the hypothesis is calculated by excel formula as =NORM.S.INV(0.99)

so, Z crit=2.33

So, the rejection region is:

A. Reject Ho if Z>2.33

c) The Z test score is calculated as:

р-ро уро (1 – ро)/п 0.09 – 0.07 0.07 (1 – 0.07) /300 = 1.358

Z=1.36

d) Conclusion/ Decision:

Since Z<Z-crit =2.33 Do not reject the null hypothesis. There is not enough evidence to support the claim.