Question 1077021
Let p = population proportion of people who talk to their pets  on the answering machine or telephone. The initial survey claims that p = 0.39, so the null hypothesis is {{{H[0]: p = 0.39}}}


In contrast, the alternative hypothesis is where the veterinarian is making the claim that the value of p is too high. Therefore, the veterinarian believes p should be lower than 0.39, so the alternative hypothesis is {{{H[1]: p < 0.39}}}. This means we have a <font color = blue>left tailed test</font>. This fact is important to figure out the p value.


Summarizing things so far, we know


Null Hypothesis:
{{{H[0]: p = 0.39}}}
Alternative Hypothesis
{{{H[1]: p < 0.39}}}
This is a <font color = blue>left tailed test</font>


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Next we need to find the test statistic. Use the formula below


{{{z = (phat - p)/(SE)}}}


where, 


{{{phat}}} = sample proportion = x/n = 54/150 = 0.36
p = hypothesized population proportion
{{{SE = sqrt(p*(1-p)/n)}}}


Let's calculate the standard error (SE) first. Plug in p = 0.39 and the sample size n = 150 to get


{{{SE = sqrt(p*(1-p)/n)}}}


{{{SE = sqrt(0.39*(1-0.39)/150)}}}


{{{SE = 0.03982461550348}}}


Which then tells us that...


{{{z = (phat - p)/(SE)}}}


{{{z = (0.36 - 0.39)/(0.03982461550348)}}}


{{{z = -0.75330294142773}}}


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The test statistic is approximately {{{z = -0.75330294142773}}}. The p value is going to be equal to the area under the standard normal curve to the <font color = blue>left</font> of this test statistic. 


We can use a table or a calculator to find this approximate area. I recommend using <a href = "https://www.wolframalpha.com/input/?i=normalcdf(-99,+-0.75330294142773)">calculator</a> which reports approximately 0.2256


The p value is approximately <font color=red>0.2256</font>


Since the p value is larger than alpha = 0.1, this means that we fail to reject the null. We must accept that p = 0.39. We don't have enough evidence to overturn it.