Question

Test the claim that the proportion of people who own cats is larger than 30% at the 0.01 significance level.

The null and alternative hypothesis would be:

The test is: right-tailed two-tailed left-tailed

Based on a sample of 600 people, 33% owned cats The test statistic is: (to 2 decimals)

The p-value is: (to 2 decimals)

Based on this we: (a)Fail to reject the null hypothesis or (b)Reject the null hypothesis

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H₀ : p = 0.30

H_a : p > 0.30

= 0.01

n = 600

= 33% = 0.33

P₀ = 0.30

1 - P₀ = 1- 0.30 = 0.70

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

=0.33- 0.30 / [0.30*(0.70) /600 ]

= 1.60

P(z >1.60 ) = 1 - P(z <1.60 ) = 0.11

P-value = 0.11

= 0.01    

p = 0.11 ≥ 0.01, it is concluded that the null hypothesis is not rejected.

Fail to reject the null hypothesis .