Answer:
The conclusion is that people are less likely to prefer dog food over all human food than would be expected by chance
Step-by-step explanation:
From the question we are told that
The sample size for first sample is [tex]n_1 = 18[/tex]
The sample size for second sample is [tex]n_2 = 18[/tex]
The number that ranked the dog food first [tex]d = 2[/tex]
The number that chose one of the other items is [tex]h = 16[/tex]
The sample proportion for first sample is
[tex]p(d) = \frac{d}{n}[/tex]
=> [tex]p(d) = \frac{2}{18}[/tex]
=> [tex]p(d) = 0.11[/tex]
The sample proportion for second sample is
[tex]p(h) = \frac{h}{n}[/tex]
[tex]p(h) = \frac{16}{18}[/tex]
[tex]p(h) = 0.8889[/tex]
The value of the pooled proportion is evaluated as
[tex]\= p = \frac{h+d}{18 +18}[/tex]
[tex]\= p = \frac{2+16}{18 +18}[/tex]
[tex]\= p = 0.5[/tex]
[tex]H0: p(d) = p(h)[/tex]
[tex]Ha : p(d) < p(h)[/tex]
Test statistics
[tex]z = \frac{(p(d)) - (p(h))}{\sqrt{\= p (1- \= p) (\frac{1}{n_1} + \frac{1}{n_2} )} }[/tex]
[tex]z = \frac{ 0.1111 - 0.8889}{\sqrt{0.5 (1- 0.5) (\frac{1}{18} + \frac{1}{18} )} }[/tex]
[tex]z = -4.67[/tex]
So since the test statistics is within the rejection region for the left tailed test
The null hypothesis is rejected
The conclusion is that people are less likely to prefer dog food over all human food than would be expected by chance
