Question

Practice Concluding a Hypothesis Test

For each of the scenarios below complete the following:

- Identify the null and alternative hypothesis.

- State if the results are statistically significant and why

- Conclude the hypothesis test in context

1. We are interested in answering the question: In Richmond Kentucky, are less than 75% of stray dogs spayed/neutered? A random sample of 150 stray dogs found that 70% were spayed/neutered. The test was performed at the 10% significance level and the resulting p-value was 0.051.

2. We are interested in answering the question: In Richmond Kentucky, is the proportion of stray dogs who are spayed/neutered less than the proportion of stray cats who are spayed/neutered? A random sample of 50 stray dogs found that 39% were spayed/neutered and a random sample of 45 cats found that 45% were spayed/neutered. The test was performed at the 5% significance level and the resulting p-value was 0.012.

3. We are interested in answering the question: Is the average price of Pepsi 2-Liter bottles in Kentucky less than 99 cents? A sample of 75 stores selling Pepsi 2-liters found an average price of 96 cents. The test was performed at the 1% significance level and the resulting p-value was 0.0065.

4. We are interested in answering the question: Is the average price of Pepsi 2-Liter bottles in Kentucky greater than the average price of Coke 2-liters in Kentucky? A random sample of 75 stores selling Pepsi was selected and a separate random sample of 55 stores selling Coke 2-liters found x pepsi - x coke cents. The test was performed at the 7% significance level and the resulting p-value was 0.092.

5. A researcher believes that if patients with arthritis go to physical therapy twice a week their pain levels will be lower than usual pain levels. Patients with arthritis usually rate their pain a 3.5 on an 8-point scale. The test was performed at the 10% significance level and the resulting p-value was 0.113.

6. The principal at Madison Central High school claims that the students at the school are above average intelligence. A random sample of thirty students IQ scores have a mean score of 112. On average the population IQ is 100. The test was performed at the 5% significance level and the resulting p-value was 0.07.

7. A neonatal nurse suspects that newborn babies are more likely to be boys than girls. A random sample found 13,173 boys were born among 25,468 newborn children. The test was performed at the 2% significance level and the resulting p-value was 0.0132.

Answer 1

1)
H0 : p = 0.75
Ha : p < 0.75

The results are statistically significant because p value is less than significance level

There is sufficient evidence to support the claim that the In Richmond Kentucky, are less than 75% of stray dogs spayed/neutered

2)
H0 : p1 = p2
Ha ; p1 < p2

The results are statistically significant because p value is less than significance level

There is sufficient evidence to support the claim that the proportion of stray dogs who are spayed/neutered less than the proportion of stray cats who are spayed/neutered

3)
H0 : mu = 99
Ha ; mu < 99

The results are statistically significant because p value is less than significance level

There is sufficient evidence to support the claim that the the average price of Pepsi 2-Liter bottles in Kentucky less than 99 cents

4)
H0 : mu1 = mu2
Ha : mu1 > mu2

The results are not statistically significant because p value is greater than significance level

There is not sufficient evidence to support the claim that the the average price of Pepsi 2-Liter bottles in Kentucky greater than the average price of Coke 2-liters in Kentucky