Question

1) Test the claim that the proportion of people who own cats is smaller than 80% at the 0.01 significance level.

a) The null and alternative hypothesis would be:

H0:p=0.8
H1:p≠0.8

H0:μ=0.8
H1:μ≠0.8

H0:μ≤0.8
H1:μ>0.8

H0:p≥0.8
H1:p<0.8

H0:μ≥0.8
H1:μ<0.8

H0:p≤0.8
H1:p>0.8

b) The test is:

2) Based on a sample of 500 people, 75% owned cats

a) The test statistic is: ________ (to 2 decimals)

b) The p-value is: _________ (to 2 decimals)

3) Based on this we:

Reject the null hypothesis

or

Fail to reject the null hypothesis

Answer 1

n= 500, = 0.75,   P = 80% = 0.80, = 0.01

1)

a)

The null and alternative hypothesis is

Ho: P    0.8

H1: P <  0.8

b)

The test is: one sample Proportion z test

2)

a)

formula for test statistics is

test statistics: z = -2.80

b)

calculate P-Value

P-Value = P(z < -2.80)

using z table we get

P(z < -2.80) = 0.0026

P-Value = 0.0026

rounding to 2 decimal

P-Value = 0

3)

decision rule is

Reject Ho if ( P-value ) ( )

here, ( P-value= 0 ) < ( = 0.01)

Hence, we can say,

Reject the null hypothesis