Practice Setting Up the Null and Alternative Hypotheses For each of the scenario

Question

Practice Setting Up the Null and Alternative Hypotheses

For each of the scenarios below identify the null and alternative hypothesis.

1. We are interested in answering the question: In Richmond Kentucky, are more than 75% of stray dogs spayed/neutered? A random sample of 250 stray dogs found that 79% were spayed/neutered.

2. We are interested in answering the question: In Richmond Kentucky, is the proportion of stray dogs who are spayed/neutered greater than the proportion of stray cats who are spayed/neutered? A random sample of 50 stray dogs found that 69% were spayed/neutered and a random sample of 45 cats found that 45% were spayed/neutered.

3. We are interested in answering the question: Does the average price of Pepsi 2-Liter bottles in Kentucky differ from 99 cents? A sample of 75 stores selling Pepsi 2-liters found an average price of 98 cents.

4. We are interested in answering the question: Does the average price of Pepsi 2-Liter bottles in Kentucky differ from 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.

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 level. Patients with arthritis usually rate their pain a 4.5 on an 8-point scale.

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.

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. (Hint: To be more likely suggest that there is more than a 50% chance of being male.)

Explanation / Answer

1)
H0 : p = 0.75
ha : p > 0.75

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

3)
H0 : mu = 99
Ha ; mu not equals to 99

4)
H0 : mu1 = mu2
Ha : mu1 not equals to mu2

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