You want to see if the percentage of cat owners is significantly less than the percentage of dog owners at a significance level of α=0.10α=0.10. You sample 700 people and find 584 have cats. You sample an additional 739 people and find 635 have dogs. What is the critical value for this test? (Report answer accurate to three decimal places.) critical value =  What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic =

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You want to see if the percentage of cat owners is significantly less than the percentage of dog owners at a significance level of α=0.10α=0.10.



You sample 700 people and find 584 have cats. You sample an additional 739 people and find 635 have dogs.

What is the critical value for this test? (Report answer accurate to three decimal places.)
critical value = 

What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic = 

Expert Solution
Step 1

Given,

Sample size of first group n1=700

Sample of people having cats X1=584

Sample size of first group n2=739

Sample of people having dogs X2=635

Level of significance α=0.10

Sample proportion of the people having cats is

p1=X1n1   =584700   =0.834

Sample proportion of the people having dogs is

p2=X2n2   =635739   =0.859

 

Step 2

Hypotheses:

H0: The percentage of cat owners is not significantly less than the percentage of dog owners.

H1: The percentage of cat owners is significantly less than the percentage of dog owners.

The test is a left tailed test.

Step 3

Critical value:

Use the EXCEL formula, "=NORMSINV(0.1)". The value obtained is -1.281.

Thus, the critical value is -1.281.

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