Question

Test the claim that the proportion of people who own cats is significantly different than 10% at the 0.05 significance level.

The null and alternative hypothesis would be:

H0:p≤0.1H0:p≤0.1
H1:p>0.1H1:p>0.1

H0:μ≤0.1H0:μ≤0.1
H1:μ>0.1H1:μ>0.1

H0:μ=0.1H0:μ=0.1
H1:μ≠0.1H1:μ≠0.1

H0:p≥0.1H0:p≥0.1
H1:p<0.1H1:p<0.1

H0:μ≥0.1H0:μ≥0.1
H1:μ<0.1H1:μ<0.1

H0:p=0.1H0:p=0.1
H1:p≠0.1H1:p≠0.1

The test is:

right-tailed

two-tailed

left-tailed

Based on a sample of 100 people, 3% owned cats

The p-value is:  (to 2 decimals)

Based on this we:

• Fail to reject the null hypothesis
• Reject the null hypothesis

Get help: Video

Box 1: Select the best answer

Box 2: Select the best answer

Box 3: Enter your answer as an integer or decimal number. Examples: 3, -4, 5.5172
Enter DNE for Does Not Exist, oo for Infinity

Box 4: Select the best answer

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.10

H_a : p 0.10

= 0.03

n = 100

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.03 - 0.10 / [(0.10 * 0.90) / 100]

= -2.33

P(z < -2.33) = 0.0099

P-value = 2 * 0.0099 = 0.0198 = 0.02

= 0.05

P-value <

Reject the null hypothesis .