Question

# Test the claim that the proportion of people who own cats is smaller than 70% at...

Test the claim that the proportion of people who own cats is smaller than 70% at the 0.10 significance level.

The null and alternative hypothesis would be: H 0 : p ≤ 0.7 H 1 : p > 0.7 H 0 : p = 0.7 H 1 : p ≠ 0.7 H 0 : μ = 0.7 H 1 : μ ≠ 0.7 H 0 : μ ≥ 0.7 H 1 : μ < 0.7 H 0 : μ ≤ 0.7 H 1 : μ > 0.7 H 0 : p ≥ 0.7 H 1 : p < 0.7

The test is: right-tailed left-tailed two-tailed Based on a sample of 500 people, 69% owned cats

The test statistic is: (to 2 decimals) The p-value is: (to 2 decimals)

Based on this we: Fail to reject the null hypothesis Reject the null hypothesis

Solution :

This is the left tailed test .

The null and alternative hypothesis is

H0 : p = 0.70

Ha : p < 0.70

= 0.69

n = 500

P0 = 0.70

1 - P0 = 1 -0.70 =0.30

Test statistic = z

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

=0.69 - 0.70 / [0.70*(0.30) /500 ]

= -0.49

P(z < -0.49) = 0.3121 = 0.31

P-value = 0.31

= 0.10

0.31 > 0.10

Fail to reject the null hypothesis .

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