Aveterinarian wants to know if pit bulls or golden retrievers have a higher incidence of tooth decay at the age of three. the vet surveys 120 three-year old pit bulls and finds 30 of them have tooth decay. the vet then surveys 160 three-year old golden retrievers and finds 32 of them have tooth decay. number the population of pit bulls and golden retrievers by 1 and 2, respectively. refer to exhibit 10.12. at the 10% significance level, can the vet conclude the proportion of pit bulls that have tooth decay is different than the proportion of golden retrievers that have tooth decay?

Comparing the p value with the significance level given we see that so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can't say that the we have significant differences between the two proportions.  

Step-by-step explanation:

1) Data given and notation

represent the number of old pit bulls with tooth decay

represent the number of golden retrievers  with tooth decay

sample selected for 1

sample selected for 2  

represent the proportion of old pit bulls with tooth decay

represent the proportion of golden retrievers  with tooth decay

z would represent the statistic (variable of interest)  

represent the value for the test (variable of interest)  

significance level given

2) Concepts and formulas to use  

We need to conduct a hypothesis in order to check if is there is a difference between the two proportions, the system of hypothesis would be:  

Null hypothesis:  

Alternative hypothesis:  

We need to apply a z test to compare proportions, and the statistic is given by:  

  (1)  

Where  

3) Calculate the statistic  

Replacing in formula (1) the values obtained we got this:  

4) Statistical decision

Since is a two side test the p value would be:  

Comparing the p value with the significance level given we see that so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can't say that the we have significant differences between the two proportions.  

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