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. 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.

2. 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.

3. 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. Null : Pain levels of arthritis patients who do not go for physical therapy twice a week and who go for physical therapy twice a week are same.

Alternate : Pain levels of arthritis patients who go for physical therapy twice a week is less than those, who do not go for physical therapy twice a week.

Results are not statistically significant because p-value is greater than the significance level. 0.113 > 0.1 .

Conclusion: Given data doesn't provide sufficient evidence to conclude that the Pain levels of arthritis patients who go for physical therapy twice a week is less than those, who do not go for physical therapy twice a week.

2. Null: Students of Madison school has same mean IQ score as the overall population of students.

Alternate : Students of Madison school has higher mean IQ score as the overall population of students.

Results are not statistically significant because p-value is greater than the significance level. 0.07 > 0.05 .

Conclusion: Given data doesn't provide sufficient evidence to conclude that the mean IQ score of madison school students is higher than population mean IQ score.

3. Null : A newborn baby is equally likely to be a boy as well as a girl.

Alternate : A newborn baby is more likely to be a boy than a girl.

The Results are statistically significant because p-value is lesser than the significance level. 0.0132 < 0.02 .

Conclusion : The given data indeed provides sufficient evidence to conclude that the a newborn baby is more likely to be a boy than a girl.

Dear student,

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