Question

according to recent poll 20% of americans think now is a good time to fid a quality job . wee want to see if percent is dufferent for tahoe residents. u servey 240 residents . use 10% level of sig .

state apropruate hypothesis

conduct approprat test

sate conclusion in cotext

disscuss whether type 1 or 2 error.

36 think now is a good time

Answer 1

Answer)

Null hypothesis Ho : u = 0.2 (20%)

Alternate hypothesis Ha : u is not equal to 0.2 (20%)

Claimed p = 0.2

Observed p = 36/240 = 0.15

N = sample size = 240

First we need to check the conditions of normality.

If np and n(1-p) both are greater than 5 or not.

n*p = 36

n*(1-p) = 204

As both are greater than 5, we can use standard normal z table to conduct the test.

Test statistics z = (observed p - claimed p)/standard error

Standard error = √claimed p*(1-claimed p)/√n

Z = -1.94

P(z<-1.94) = 0.0262

But this is for one tail and our test is two tailed

So,the required p-value is = 2*0.0262 = 0.0524

As the obtained p-value is less than the given significance level, 0.1 (1%)

We reject the null hypothesis.

So, we have enough evidence to support the claim that proportion is different.

Type 1 error means, rejecting true null hypothesis.

Type 2 error means, failure to reject the false null hypothesis

Here, observed p is 0.15

And claimed is 0.20

And they both are different, so our conclusion is right.