Use the given sample sizes and numbers of successes to compl

Use the given sample sizes and numbers of successes to complete a significance test that is testing if there is a difference between the proportion of household with and without a dog that are burglarized. Assume that you plan to use a significance level of a = 0.05 to test the claim. A report on the nightly news broadcast stated that 13 out of 178 households with pet dogs were burglarized and 23 out of 213 households without pet dogs were burglarized. Is there one population of qualitative populations? Is the data quantitative or qualitative data? Will you use a stats or proportion stats in statcrunch? Stats the null and alternative hypothesis, H_0 and H Give the value of the test statistic rounded to 2 decimal places. Give the p-value rounded to 4 decimal places. Should your decision be to reject H_0 or do not reject H_0? Give a correctly formatted significance test conclusion in sentence form.

Solution

1.

There are 2 populations, the first population being those household with dogs and the second being those without dogs.

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2.

It is quantitative data, in terms of proportions. [QUANTITATIVE]

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3.

This is a proportions test, so PROPORTION STATS. [ANSWER]

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4.

Let p1 and p2 be the proportions for with and without dogs, respectively.

Formulating the hypotheses          
Ho: p1 - p2   =   0  
Ha: p1 - p2   =/=   0   [ANSWER]

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5.

Here, we see that pdo =    0   , the hypothesized population proportion difference.  
          
Getting p1^ and p2^,          
          
p1^ = x1/n1 =    0.073033708      
p2 = x2/n2 =    0.107981221      
          
Also, the standard error of the difference is          
          
sd = sqrt[ p1 (1 - p1) / n1 + p2 (1 - p2) / n2] =    0.028853915      
          
Thus,          
          
z = [p1 - p2 - pdo]/sd =    -1.211187882 = -1.21   [ANSWER, TEST STATISTIC]  
          
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6.

          
Also, the p value is, as this is two tailed,          
          
P =    0.225823406   [ANSWER]

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7.

As P > 0.05, we DO NOT REJECT HO.

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8.  
          
There is no significant evidence that there is a difference between the proportion of households burglarized between those with dogs and those without. [CONCLUSION]