Question

Cody is an environmental scientist inquiring about the percentage of deer ticks in a certain national park that are infected with Lyme disease. He suggests that more than 28% of the deer ticks in the park are infected with the disease. Cody randomly selects deer ticks from various spots throughout the park and tests each one for the presence of the disease. Of the 141 deer ticks Cody selected, 43 were infected with Lyme disease. Are all of the conditions for this hypothesis test met, and if so, what are the null and alternative hypotheses for this hypothesis test?

Answer 1

Answer:

In order to apply the z proportion test we need to verify the following conditions:

1) Randomization we need a random sample.

2) 10 % condition we need that the sample size would be lower than 10% of the population size

3) We need  to satisfy the normalyti condition:

n⋅p≥10 and n⋅(1−p)≥10

And for this case we satisfy all the conditions

We need to conduct a hypothesis in order to test the claim that the true proportion is higher than 0.28, so the correct system of hypothesis are:  

Null hypothesis:$p \leq 0.28$  

Alternative hypothesis:$p > 0.28$  

Step-by-step explanation:

Data given and notation

n=141 represent the random sample taken

X=43 represent the adults that were infected with Lyme disease

$\hat p=\frac{43}{141}=0.305$ estimated proportion of adults infected with Lyme disease

$p_o=0.28$ is the value that we want to test

$\alpha=$ represent the significance level

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)  

Solution to the problem

In order to apply the z proportion test we need to verify the following conditions:

1) Randomization we need a random sample.

2) 10 % condition we need that the sample size would be lower than 10% of the population size

3) We need  to satisfy the normalyti condition:

n⋅p≥10 and n⋅(1−p)≥10

And for this case we satisfy all the conditions

We need to conduct a hypothesis in order to test the claim that the true proportion is higher than 0.28, so the correct system of hypothesis are:  

Null hypothesis:$p \leq 0.28$  

Alternative hypothesis:$p > 0.28$