Question

An education researcher claims that at most 8% of working college students are employed as teachers or teaching assistants. In a random sample of 200 working college students, 10% 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 Ha 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. The percentage of working college students who are employed as teachers or teaching assistants is not %. O B. At most % of working college students are employed as teachers or teaching assistants. OC. % of working college students are employed as teachers or teaching assistants OD. More than % 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 Ho and Ha Select the correct choice below and fill in the answer boxes to complete your choice. (Round to two decimal places as needed.) O A. Hops OB. Ho.pt OC. Hop Ha:p> Ha: p= Hap+ OD. Ho:p> O E. Ho:p> OF. Hop2 Ha:ps Ha:p2 Ha:p

Answer 1

Solution:

a)

Identify the claim

Answer : B. At most 8 %of working college students are

State H₀ and H_a

H₀ : p  $\leq$ 0.08

H_a : p > 0.08

b)

$\alpha$ = 0.01

> sign in Ha indicates that the test is "Right tailed "

So , critical value is

2a 20.01 2.33

z₀ = 2.33

Identify the rejection regions.

The rejection region is z > 2.33

c)

n = 200

Let  $url=https://latex.codecogs.com/gif.latex?%5Chat%20p&t=1596167392&ymreqid=f4764063-0d40-e2b0-1cde-f0008d012f00&sig=sTtj6fUQ557EVceE5O50Rw--~D$ be the sample proportion.

$url=https://latex.codecogs.com/gif.latex?%5Chat%20p&t=1596167392&ymreqid=f4764063-0d40-e2b0-1cde-f0008d012f00&sig=sTtj6fUQ557EVceE5O50Rw--~D$ = x/n = 10% = 0.10

The test statistic z is

z =   $url=https://latex.codecogs.com/gif.latex?%5Cfrac%7B%5Chat%20p-p%7D%7B%5Csqrt%7B%5Cfrac%7Bp%281-p%29%7D%7Bn%7D%7D%7D&t=1596167392&ymreqid=f4764063-0d40-e2b0-1cde-f0008d012f00&sig=3WpFpTtEmFdUVRm2kKWcfg--~D$

=  (0.10 - 0.08)/$\sqrt{}$[0.08*(1 - 0.08)/200]

= 1.04

z = 1.04

d)

Fail to reject the null hypothesis. There is not enough evidence to reject the researcher's claim