Question

2. 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.

3. 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.

4. 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

Q2) We are testing here whether the mean price is less than 99 cents. The p-value for the test is given to be 0.0065 < 0.01 which is the level of significance, therefore the test is significant here and we can reject the null hypothesis here. Therefore we have sufficient evidence here that the mean price is indeed less than 99 cents ( at the 1% level of significance. )

Q3) As the p-value here for the test is 0.113 > 0.1 which is the level of significance, therefore the test is not significant and we have insufficient evidence that the patients with arthritis go to physical therapy twice a week their pain levels will be lower than usual pain levels. Note that we cannot reject the null hypothesis here.

Q4) As the p-value here is 0.0132 < 0.02 which is the level of significance, therefore the test is significant and therefore we have sufficient evidence here that the newborn babies are more likely to be boys than girls. We are rejecting the null hypothesis here.