Question

Lee is a teacher at a local high school who wanted to assess whether or not dogs physically resemble their owners enough for people to be able to correctly match a dog to their owner better than if just guessing. Lee, who is also a dog owner, showed pictures of two dogs to her class of 16 students. One photo was of the teacher's dog (Yoda) and the other photo was of a dog the teacher had never met. The students were asked to guess which dog was actually the teacher's. If dogs do not physically resemble their owners, the students would get a correct match with probability 0.50. It turned out that 14 of the 16 students correctly picked out the teacher's dog.

Does it appear that the population proportion of people who can correctly match a dog to their owner (out of two options) is better than just guessing?

Answer 1

The decision rule is

Reject the null hypothesis

The conclusion is

There is sufficient evidence to conclude that the population proportion of people who can correctly match a dog to their owner (out of two options) is better than just guessing

Explanation:

From the question we are told that

The sample size is n = 16

The population proportion = 0.5

The number that of students that picked out the teachers dog is k = 14

Generally the sample proportion is mathematically represented as

`\^ p  =(k)/(n)`

=>
`\^ p  =(14)/(16)`

=>
`\^ p  = 0.875`

The null hypothesis is
`H_o :  p = 0.5`

The null hypothesis is
`H_o :  p >  0.5`

Generally the test statistics is mathematically represented as

`z  =  \frac{\^  p  -  p }{\sqrt{ (p(1- p ))/(n) }  }`

`z  =  \frac{0.875   -  0.50 }{\sqrt{ (0.50 (1- 0.50 ))/(16) }  }`

`z  = 3`

Generally the p-value is mathematically represented as

`p-value  =  P(Z > 3)`

From the z table the probability of Z>3 is mathematically represented as

`P(Z > 3) =  0.0013499`

So

`p-value  =  0.0013499`

Let assume the level of significance is
`\alpha = 0. 05`

Generally from the value obtained we see that
`p-value  <  \alpha` Hence

The decision rule is

Reject the null hypothesis

The conclusion is

There is sufficient evidence to conclude that the population proportion of people who can correctly match a dog to their owner (out of two options) is better than just guessing