You recently moved to Canada for a new job and have been noticing the number of
ID: 3305999 • Letter: Y
Question
You recently moved to Canada for a new job and have been noticing the number of people with pets seems higher than you remember in the United States. You do some digging, and find that in the US, the proportion of houses that own dogs is 0.365, cats 0.304, and other/none the rest. (source: 2012 U.S. Pet Ownership and Demographics Sourcebook, American Veterinary Medical Association).
What is your research question?
Describe how you could take a sample in your new home to compare against the data you found.
What type of study is this?
What is your variable of interest and what type of variable is it?
You perform your sample of 60 homes and find that 23 households own cats, and 19 own dogs. (source: Canadian Pet Market Outlook, 2014).
What type of test can you perform on this data? Justify your answer.
What is the null and alternative hypothesis?
Calculate your test statistic, degrees of freedom and the p-value.
Interpret your results.
Were all the assumptions met to have performed this test? Is there any additional information you might need to be sure all the assumptions were met?
Explanation / Answer
What is your research question?
Answer : Does proportion of Canadaiian people owning pets is higher the proportion of AMerican People owning pets?
Describe how you could take a sample in your new home to compare against the data you found.
Answer : I will do a random sampling in this case. I will earmark random homes in my locality and some surronding homes by looking their phone number for their phone direcctory and their address.
What type of study is this?
ANswer : The study is an observation study.
What is your variable of interest and what type of variable is it?
Answer : Variable of interest here is the number of the families in Canada those who own a pet. THe variable is dichotomous or nominal Variable.
What type of test can you perform on this data? Justify your answer.
Answer : We will perform hypothesis testing for proportions for the given data.
What is the null and alternative hypothesis?
Null HYpothesis : H0 : There is no difference in proportion of Canada people who own pets as compared to proportion of US people. pcanada = pUS
Alternative Hypothesis : Ha : Proportion of Canada people who own pets are higher than the proportion of US people who owns pets. pcanada > pUS
Calculate your test statistic, degrees of freedom and the p-value.
here p0 = 0.365 + 0.304 = 0.669
sample proportion p^ = (23 + 19)/ 60 = 0.7
so Z = (p^ - p0 )/ sqrt (p0 * (1-p0 )/ N]
Z = ( 0.7 - 0.669)/ sqrrt (0.669 * 0.331 / 60)
Z = 0.031/ 0.06075 = 0.51
p - value = Pr( Z > 0.51) = 1 - 0.6950 = 0.305
Interpret your results.
Here p - value > 0.05 so we cannot reject the null hypothesis and we can concude that There is no difference in proportion of Canada people who own pets as compared to proportion of US people.
Were all the assumptions met to have performed this test? Is there any additional information you might need to be sure all the assumptions were met?
Assumptions here are np >= 10 and nq >= 10
that means that number of positives like number of pet owners was greater than 10 and number of non-pet owners were also were greater than 10.
Random samling was also performed.
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