Question

Dr. Java wants to know if students study statistics better after drinking coffee compared to after drinking water. Fifteen students are given a cup of coffee, then study statistics for an hour. They rate their studying as an average of 8.00. The next day, the same students were given a glass of water, then studied statistics for an hour. They rate their studying as an average of 7.50. Using an ŜD = 1.75 and an alpha of .05, and do this correlated samples t-test by hand.

Answer 1

To conduct a correlated samples t-test by hand, we need to start by formulating the null hypothesis (H0) and alternative hypothesis (Ha). We then calculate the t-test statistic and determine the degrees of freedom (df) to find the critical t-value for the given alpha level.

Step-by-step explanation:

To conduct a correlated samples t-test by hand, we need to start by formulating the null hypothesis (H0) and alternative hypothesis (Ha). In this case, the null hypothesis states that there is no difference in studying statistics after drinking coffee compared to after drinking water, while the alternative hypothesis states that there is a difference. We calculate the t-test statistic using the formula:

t = (mean of coffee - mean of water) / (standard deviation / square root of sample size).

Next, we determine the degrees of freedom (df) using the formula:

df = sample size - 1.

We then use the t-distribution table or a statistical calculator to find the critical t-value at the given alpha level. If the calculated t-value is greater than the critical t-value, we reject the null hypothesis and conclude that there is a significant difference in studying statistics after drinking coffee compared to after drinking water.