Question

Test the claim that the proportion of people who own cats is smaller than 80% at the 0.05 significance level The null and alternative hypothesis would be: H: H: = 0.8 H.:P = 0.8 H.:P = 0.8 >0.8 Hp > 0.8 H P 0.8 H:u=0.8 H.:P = 0.8 H: = 0.8 0.8 H:p < 0.8 H H < 0.8 O The test is: left-tailed right-tailed two-tailed O Based on a sample of 200 people, 146 owned cats What is pto 2 decimal places)? The test statistic is: (to 2 decimals)

Answer 1

Hypothesis: $H_0:p=0.80$ VS  $H_a:p<0.80$

The test is one tailed test

Gievn : n=200 , X=148 , The estimate of the sample proportion is , $\hat{p}=\frac{X}{n}=\frac{146}{200}=0.73$

The test statistic is ,

$Z_{stat}=\frac{\hat{p}-p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}=\frac{0.73-0.80}{\sqrt{\frac{0.80(1-0.80)}{200}}}=-2.47$

The p-value is ,

p-value=$P(Z>|Z_{stat}|)=P(Z>2.47)=1-P(Z\leq 2.47)=1-\Phi(2.47)$

; From standard normal distribution table

=1-0.9932 = 0.0068

Decision : Here , p-value=0.0068<0.05

Therefore , reject the null hypothesis.

Conclusion : Hence , there is sufficient evidence to support the claim that the proportion of people who own cars is smaller than 80% .