Question

Test the claim that the proportion of people who own cats is significantly different than 20% at the 0.01 significance level.

The alternative hypothesis would be:

μ>0.2

p≠0.2

μ≠0.2

p>0.2

p<0.2

μ<0.2

The test is:

right-tailed

two-tailed

left-tailed

Based on a sample of 500 people, 16% 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

The conclusion is:

• At the 0.01 alpha level, I was unable to show that the proportion of people who own cats is significantly different than 20 percent.
• At the 0.01 alpha level, I was able to show that the proportion of people who own cats is significantly less than 20 percent.
• At the 0.01 alpha level, I was unable to show that the proportion of people who own cats is significantly greater than 20 percent.
• At the 0.01 alpha level, I was able to show that the proportion of people who own cats is equal to 20 percent.
• At the 0.01 alpha level, I was unable to show that proportion of people who own cats is significantly less than 20 percent.
• At the 0.01 alpha level, I was able to show that the proportion of people who own cats is significantly greater than 20 percent.

Answer 1

The alternative hypothesis is

Ha: p 0.2

The test is two tailed

Test statistics

z = ( - p) / sqrt [ p ( 1 - p) / n ]

= (0.16 - 0.20) / sqrt ( 0.20 ( 1 - 0.20) / 500)

= -2.34

p-value = 2 * P(Z < z)

= 2 * P(Z < -2.34)

= 2 * 0.0096

= 0.0192

Since p-value > 0.01 level, do not reject H0.

Conclusion -

At the 0.01 alpha level, I was unable to show that the proportion of people who own cats is significantly

different than 20 percent.