Is a new hair shampoo product actually effective? Ask participants to grade themselves on scale of 1-10 how attractive their hair is both before and after using a shampoo product after 2 weeks

Results

Subject Initial Rating (A) Rating After 2 Weeks (B)
1 1 5
2 2 3
3 5 5
4 3 7
5 6 5
6 3 6

give the values of the test statistic and the p-value for this test

I have no idea which test to use: avova, chi-squared, 1-var-stats....etc
Also I tried all of these and I cannot get the answer

I have the correct answer I just cannot figure out the process to get it!
Please help! Thank you!

To determine whether a new hair shampoo product is effective, you can use a paired t-test. This type of test compares two sets of measurements obtained from the same sample (in this case, the participants' hair attractiveness ratings).

Here's how you can calculate the test statistic and p-value for this test:

Step 1: Calculate the difference between the two ratings for each participant: B - A.

Subject Initial Rating (A) Rating After 2 Weeks (B) Difference (B - A)
1 1 5 4
2 2 3 1
3 5 5 0
4 3 7 4
5 6 5 -1
6 3 6 3

Step 2: Calculate the mean of the differences (d̄) and the standard deviation of the differences (s).

Mean of the differences (d̄) = (Σ(B - A)) / n
Standard deviation of the differences (s) = √((Σ((B - A) - d̄)^2) / (n - 1))

In this case, n (the number of participants) is 6.

Σ(B - A) = (4 + 1 + 0 + 4 - 1 + 3) = 11
d̄ = 11 / 6 ≈ 1.833

Σ((B - A) - d̄)^2 = ((4 - 1.833)^2 + (1 - 1.833)^2 + (0 - 1.833)^2 + (4 - 1.833)^2 + (-1 - 1.833)^2 + (3 - 1.833)^2) ≈ 20.833
s = √(20.833 / (6 - 1)) ≈ 1.845

Step 3: Calculate the t-value.

t = d̄ / (s / √n) = 1.833 / (1.845 / √6) ≈ 1.571

Step 4: Determine the degrees of freedom (df) and find the corresponding p-value using a t-distribution table or a statistical software.

The degrees of freedom are given by (n - 1), where n is the number of participants. In this case, the df = 6 - 1 = 5.

Using the t-distribution table or a statistical software, you can find the p-value associated with the t-value of approximately 1.571 and df = 5. This p-value will tell you the probability of obtaining these results (or more extreme) under the null hypothesis (i.e., no effect of the hair shampoo product).

If the calculated p-value is lower than your chosen significance level (e.g., 0.05), you can reject the null hypothesis and conclude that there is evidence that the hair shampoo product has an effect on the attractiveness of the hair.

Note: It seems like there might be a mistake in the data provided (Subject 5 has a negative difference). Double-check the calculations and data to ensure accuracy.