Question

Test the claim that the proportion of m en who own catsis sm aller than 90% at the .01 significance level The null and altern ative hypothesis would be: :0.9 Но:р — 0.9 Но: и — 0.9 Но:а 3 0.9 Н:р — 0.9 Н:р 3D 0.9 0.9 H:р 20.9 H:р> 0.9 Но: и Нiд <0.9 Н:р <0.9 H:д 0.9 H: The test is left-tailed right-tailed two-tailed Based on a sample of 60 people, 83% owned cats The test statistic is (to 3 decim al s) The critical v alue is (to 2 de cimals) Based on this we Reject the null hypothesis Fail to reject the null hypothesis

Answer 1

Solution :

This is the left tailed test .

The null and alternative hypothesis is

H₀ : p = 0.90

H_a : p < 0.90

= 0.83

р

Test statistic = z

=
р
- P₀ / [$\sqrt$P_{0 *} (1 - P₀ ) / n]

= 0.83 - 0.90 / [$\sqrt$(0.90 * 0.1) / 83]

Test statistic = 2.126

Critical value = -2.33

Fail to reject the null hypothesis .