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The null and alternative hypothesis would be:
- H0:P=0.2
H1:P>0.2 - H0:U=0.2
H1:U>0.2 - H0:U=0.2
H1:U≠0.2 - H0:P=0.2
H1:P<0.2 - H0:P=0.2
H1:P≠0.2 - H0:U=0.2
H1:U<0.2
Based on a sample of 45 people, 13% owned cats
The test statistic is (to 3 decimals)
The critical value is (to 2 decimals)
Based on this we
- Fail to reject the null hypothesis
- Reject the null hypothesis
Step by step
Solved in 3 steps
- Test the claim that the proportion of men who own cats is significantly different than 35% at the 0.2 significance level.The null and alternative hypothesis would be: H0:μ=H0:μ=H1:μ<H1:μ<H0:p=0.35H0:p=0.35H1:p≠0.35H1:p≠0.35 H0:μ=H0:μ=H1:μ≠H1:μ≠H0:μ=H0:μ=H1:μ>H1:μ>H0:p=0.35H0:p=0.35H1:p<0.35H1:p<0.35H0:p=0.35H0:p=0.35H1:p>0.35H1:p>0.35 The test is: right-tailed left-tailed two-tailed Based on a sample of 55 men, 255255 of the men owned catsThe test statistic is: z=z=___?___ (to 2 decimals)The positive critical value is zC=zC=1.28155.Test the claim that the proportion of men who own cats is significantly different than 20% at the 0.02 significance level. The null and alternative hypothesis would be: H0:p=0.2H0:p=0.2H1:p<0.2H1:p<0.2 H0:μ=0.2H0:μ=0.2H1:μ≠0.2H1:μ≠0.2 H0:μ=0.2H0:μ=0.2H1:μ>0.2H1:μ>0.2 H0:p=0.2H0:p=0.2H1:p≠0.2H1:p≠0.2 H0:μ=0.2H0:μ=0.2H1:μ<0.2H1:μ<0.2 H0:p=0.2H0:p=0.2H1:p>0.2H1:p>0.2 The test is: two-tailed right-tailed left-tailedTest the claim that the proportion of men who own cats is significantly different than 30% at the 0.1 significance level.The null and alternative hypothesis would be: H0:p=0.3H0:p=0.3H1:p≠0.3H1:p≠0.3 H0:p=0.3H0:p=0.3H1:p<0.3H1:p<0.3 H0:p=0.3H0:p=0.3H1:p>0.3H1:p>0.3 H0:μ=0.3H0:μ=0.3H1:μ>0.3H1:μ>0.3 H0:μ=0.3H0:μ=0.3H1:μ≠0.3H1:μ≠0.3 H0:μ=0.3H0:μ=0.3H1:μ<0.3H1:μ<0.3 The test is: two-tailed left-tailed right-tailed Based on a sample of 70 people, 21% owned catsThe test statistic is: (to 2 decimals)The positive critical value is: (to 2 decimals)Based on this we: Fail to reject the null hypothesis Reject the null hypothesis
- Test the claim that the proportion of people who own cats is significantly different than 40% at the 0.05 significance level.The null and alternative hypothesis would be: H0:p≥0.4H0:p≥0.4H1:p<0.4H1:p<0.4 H0:μ≤0.4H0:μ≤0.4H1:μ>0.4H1:μ>0.4 H0:μ≥0.4H0:μ≥0.4H1:μ<0.4H1:μ<0.4 H0:p≤0.4H0:p≤0.4H1:p>0.4H1:p>0.4 H0:p=0.4H0:p=0.4H1:p≠0.4H1:p≠0.4 H0:μ=0.4H0:μ=0.4H1:μ≠0.4H1:μ≠0.4 The test is: two-tailed left-tailed right-tailed Based on a sample of 700 people, 44% owned catsThe 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 hypothesisTest the claim that the proportion of men who own cats is significantly different than 20% at the 0.2 significance level.The null and alternative hypothesis would be: H0:p=0.2H0:p=0.2H1:p≠0.2H1:p≠0.2 H0:μ=H0:μ=H1:μ>H1:μ> H0:μ=H0:μ=H1:μ<H1:μ< H0:μ=H0:μ=H1:μ≠H1:μ≠ H0:p=0.2H0:p=0.2H1:p>0.2H1:p>0.2 H0:p=0.2H0:p=0.2H1:p<0.2H1:p<0.2 The test is: left-tailed two-tailed right-tailed Based on a sample of 65 men, 17651765 of the men owned catsThe test statistic is: z=z= (to 2 decimals)The positive critical value is zC=zC=1.28155.Thus the test statistic in the critical region.Based on this we: Reject the null hypothesis Fail to reject the null hypothesisTest the claim that the proportion of people who own cats is significantly different than 40% at the 0.05 significance level.The null and alternative hypothesis would be: H0:μ≤0.4H0:μ≤0.4H1:μ>0.4H1:μ>0.4 H0:μ≥0.4H0:μ≥0.4H1:μ<0.4H1:μ<0.4 H0:μ=0.4H0:μ=0.4H1:μ≠0.4H1:μ≠0.4 H0:p≥0.4H0:p≥0.4H1:p<0.4H1:p<0.4 H0:p=0.4H0:p=0.4H1:p≠0.4H1:p≠0.4 H0:p≤0.4H0:p≤0.4H1:p>0.4H1:p>0.4 The test is: two-tailed left-tailed right-tailed Based on a sample of 600 people, 32% owned catsThe p-value is: (to 2 decimals)Based on this we: Reject the null hypothesis Fail to reject the null hypothesis
