which test to use One-sample or independent samples t-test?

A researcher tests five individuals who have seen paid political ads about a particular issue. These individuals take a multiple-choice test about the issue in which people in general (who know nothing about the issue) usually get 40 questions correct. The number correct for these five individuals was 48, 41, 40, 51, 50. Using a .05, one-tailed test, do people who see the ads do better on this test?

I would use 1 sample here because we aren't comparing differences based on any other quality (i.e. gender)

so I will found my mean for this set by adding up all the data points and divide by 5

Yes, you will need the mean and the standard deviation of the data.

then conduct a one-tail test by comparing your mean to the mean of 40 given.

To determine whether people who see the ads do better on the test, you need to compare the performance of the five individuals who saw the ads to a standard performance level.

In this case, the standard performance level is represented by the average score of people in general who know nothing about the issue, which is 40 questions correct.

To test the hypothesis, you can use either a one-sample t-test or an independent samples t-test. Here's how you can decide which test to use:

1. One-sample t-test: Use a one-sample t-test if you want to compare the mean score of the five individuals who saw the ads to the standard performance level of 40 questions correct.

2. Independent samples t-test: Use an independent samples t-test if you want to compare the mean scores of two independent groups. In this case, you would need a separate group of individuals who did not see the ads and also took the test.

Given that you only have data for the group of individuals who saw the ads, a one-sample t-test would be appropriate here.

Steps to conduct a one-sample t-test:

1. Calculate the mean score of the five individuals who saw the ads.
2. Calculate the standard deviation of the scores of the five individuals.
3. Set up the null and alternative hypothesis:
- Null hypothesis (H0): The mean score of individuals who see the ads is equal to the standard performance level of 40 questions correct.
- Alternative hypothesis (Ha): The mean score of individuals who see the ads is greater than 40 questions correct.
4. Determine the level of significance (α) - in this case, α = 0.05.
5. Calculate the t-value using the formula:
t = (mean score - standard performance level) / (standard deviation / sqrt(sample size))
6. Calculate the degrees of freedom (df) using the formula:
df = sample size - 1.
7. Find the critical t-value corresponding to the chosen level of significance and degrees of freedom from a t-distribution table.
8. Compare the calculated t-value to the critical t-value to make a decision:
- If the calculated t-value is greater than the critical t-value, reject the null hypothesis.
- If the calculated t-value is less than or equal to the critical t-value, fail to reject the null hypothesis.

By following these steps, you can determine if people who see the ads perform better on the test compared to the standard performance level of 40 questions correct.