Question

Scenario 2

You are a psychologist who is studying the effects of the coronavirus situation on college students in America. The test you are using to measure their reactions has normally distributed results in the population where a score of less than 145 means that a college student will not have any long term adverse effects from the situation. Here are the scores from those tested: 168, 147, 121, 193, 132, 189, 114, 143, 118, 139. Can you conclude that the average college student will not have long term effects from the situation (that their mean score will be less than 145)? Use α=.03

Note: When writing this problem, I do not yet know the answer myself. This is all fake data. If it comes out as a scary answer, remember that I just made this all up.

1. In words what is the claim? Write it in symbols.

2. Write the opposite claim in symbols.

3. H₀:

H₁:

4. What is the significance level (α)?

5. Find the p-value.

6. Based on the p-value and α, do you reject the null hypothesis or do you fail to reject the null hypothesis?

7. In words, based on number 6, what can you conclude?

Scenario 3

You are a biochemist who is studying the levels of dopamine in the brain of adults with Parkinson’s disease after taking a certain medication. A healthy adult will have 60-80 pg/mL of dopamine in their blood, whereas a Parkinson’s patient will have a much lower level. A group of 150 Parkinson’s patients were given a new medication. After 1 hour, their dopamine levels were tested. It was found that the mean dopamine level was 69 pg/mL with a standard deviation of 3.8. Can we conclude that the medicine works for the patients? In other words can we claim that in the population of all Parkinson’s patients, their dopamine level after taking this medicine would be greater than or equal to 60? Use α=.01

1. In words what is the claim? Write it in symbols.

2. Write the opposite claim in symbols.

3. H₀:

H₁:

4. What is the significance level (α)?

5. Find the p-value.

6. Based on the p-value and α, do you reject the null hypothesis or do you fail to reject the null hypothesis?

7. In words, based on number 6, what can you conclude?

Answer 1

Scenario 2

Answer:

significance level = 0.03

p-value = 0.5603

Decision: fail to reject the null hypothesis

Conclusion: There is not sufficient evidence to conclude that the mean reaction score is less than 145.

Explanation:

Hypotheses

The Null and Alternative Hypotheses

This is a left-tailed test

Test statistic

The t statistic is obtained using the formula,

The mean and standard deviation values are obtained in excel. The screenshot is shown below,

p-value

The p-value is obtained from t distribution table for degree of freedom = n - 1 = 10 - 1 = 9 and for two left tailed test

p-value = 0.5603

Decision:

Since the p-value = 0.5603 is greater than the significance level = 0.03, the null hypothesis is rejected at a 3% significance level.

Conclusion:

There is not sufficient evidence to conclude that the mean reaction score is less than 145.

Scenario 3

Answer:

significance level = 0.01

p-value = 0.0000

Decision: Reject the null hypothesis

Conclusion: There is sufficient evidence to conclude that the mean dopamine level after taking this medicine would be greater than or equal to 60.

Explanation:

Hypotheses

The Null and Alternative Hypotheses

This is a right-tailed test

Test statistic

The t statistic is obtained using the formula,

p-value

The p-value is obtained from t distribution table for degree of freedom = n - 1 = 150 - 1 = 149 and for two left tailed test

p-value = 0.0000

Decision:

Since the p-value = 0.0000 is less than the significance level = 0.01, the null hypothesis is rejected at a 1% significance level.

Conclusion:

There is sufficient evidence to conclude that the mean dopamine level after taking this medicine would be greater than or equal to 60.