Q1. Manually Perform and Interpret a one-samplet-test(13 points total)

The average memory score is around 27 in the general population aged 75 and up. The participants in this project have no neurological disorders, are healthy, and are well educated so the researchers hypothesized that the individuals aged 75 or older in their research population would score significantly higher than the general population in the same age range. So, the research question here is:

Do people aged 75 or older in the research population (population 1) have significantly higher memory scores compared to those aged 75 or older in the general population (population 2)?

Select the participants who are 75 or older from the data set, and then enter their scores on memory into a separate Excel worksheet for this question set. There should be 10 data points. Follow the steps below to conduct a one-samplet-testMANUALLY, with= .05.

Hint: We know that the mean memory score for population 2 (that is, the comparison population) is₂= 27.

1. Createdirectionalalternative hypothesis and null hypothesis from the research question listed above. Type the hypotheses out both in words and in symbol notations.

(2 points total: 1 for each hypothesis. If symbol notation or written format is missing or incorrect for a hypothesis, deduct .5)

2. For the one-tailed hypothesis test with= .05:

What is the degree of freedom?(1 point, must show manual calculation process to earn the point)

Identify the criticaltvalue from thettable.(1 point, must explain how the value is obtained to earn the point)

Be sure to explain how you figure out each of the answers. No point is earned if there is no explanation or calculation process.

3. Calculate thetstatistic by following the steps below.

3a. Calculate the sample mean,M.

(1 point, must show manual calculation process to earn the point)

3b. Calculate the estimated population standard deviation,s.

(1 point, must show manual calculation process to earn the point)

3c. Calculate the standard error of the comparison distribution,s_M.

(1 point, must show manual calculation process to earn the point)

3d. Calculate thetstatistic using the results from 3a, 3b, and 3c.

(1 point, must show manual calculation process to earn the point)

4. Compare thetstatistic with the criticaltvalue to make a decision on the hypothesis test.

-Is thetstatistic more extreme than the criticaltvalue?

-Do you reject (or fail to reject) the null hypothesis?

(2 points total: 1 for each question)

5. Answer the research question based on the hypothesis test result.

(1 point)

6. Calculate the raw effect size and standardized effect size of this hypothesis test.

(2 points total: 1 for each effect size, must show manual calculation process to earn the point)