SOLUTION: In a​ survey, 39​% of the respondents stated that they talk to their pets on the answering machine or telephone. A veterinarian believed this result to be too​

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Question 1077021: In a​ survey,
39​% of the respondents stated that they talk to their pets on the answering machine or telephone. A veterinarian believed this result to be too​ high, so
randomly selected 150 pet owners and discovered that
54 of them spoke to their pet on the answering machine or telephone. Does the veterinarian have a right to be​ skeptical? Use the α=0.1 level of significance.
I'm having trouble finding the P value
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
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

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 . This means we have a left tailed test. This fact is important to figure out the p value.

Summarizing things so far, we know

Null Hypothesis:

Alternative Hypothesis

This is a left tailed test

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



where,

= sample proportion = x/n = 54/150 = 0.36
p = hypothesized population proportion


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







Which then tells us that...







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The test statistic is approximately . The p value is going to be equal to the area under the standard normal curve to the left of this test statistic.

We can use a table or a calculator to find this approximate area. I recommend using calculator which reports approximately 0.2256

The p value is approximately 0.2256

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.
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