Question

# Test the claim that the proportion of people who own cats is significantly different than 90%...

Test the claim that the proportion of people who own cats is significantly different than 90% at the 0.01 significance level. The null and alternative hypothesis would be: H 0 : p ≤ 0.9 H 1 : p > 0.9 H 0 : μ = 0.9 H 1 : μ ≠ 0.9 H 0 : μ ≤ 0.9 H 1 : μ > 0.9 H 0 : p = 0.9 H 1 : p ≠ 0.9 H 0 : p ≥ 0.9 H 1 : p < 0.9 H 0 : μ ≥ 0.9 H 1 : μ < 0.9 The test is: two-tailed left-tailed right-tailed Based on a sample of 300 people, 95% owned cats The test statistic is: (to 2 decimals) The p-value is: (to 2 decimals) Based on this we: Reject the null hypothesis Fail to reject the null hypothesis

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H0 : p = 0.90

Ha : p 0.90

= 0.95

Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

= 0.95 - 0.90 / [(0.90 * 0.10) / 300]

= 2.89

P(z > 2.89) = 1 - P(z < 2.89) = 0.0039

P-value = 0.004

= 0.01

P-value <

Reject the null hypothesis .