stuck on steps 2 and 4 of hypothesis testing. Need a formula to complete. please help...
A researcher theorized that people can hear better when they have just eaten a large meal. Six individuals were randomly assigned to eat either a large meal or a small meal. After eating the meal, their hearing was tested. The hearing ability scores (high numbers indicate greater ability) are given in the following table. Using the .05 level, do the results support the researcher’s theory? (a) Use the steps of hypothesis testing, (b) sketch the distributions involved.
Big Meal Group Small Meal Group
Subject Hearing Subject Hearing
A 22 D 19
B 25 E 23
C 25 F 21
Determine the characteristics of the comparison distributions.
Mean = 0
standard deviation??
Step 4: Determine your samples score on the comparison distribution.
To determine the characteristics of the comparison distributions, we need to calculate the mean and standard deviation for both the big meal group and the small meal group.
To calculate the mean, add up all the hearing scores in each group and divide by the number of individuals in that group.
For the big meal group:
Mean = (22 + 25 + 25) / 3 = 24
For the small meal group:
Mean = (19 + 23 + 21) / 3 = 21
Now, to calculate the standard deviation, we need to find the variance first. The variance measures how spread out the data is. Then we can take the square root of the variance to get the standard deviation.
To calculate the variance, we need to find the deviation of each hearing score from the mean, square each deviation, sum them up, and divide by the number of individuals minus 1.
For the big meal group:
Deviation from mean: (22 - 24) = -2, (25 - 24) = 1, (25 - 24) = 1
Squared deviations: (-2)^2 = 4, 1^2 = 1, 1^2 = 1
Sum of squared deviations: 4 + 1 + 1 = 6
Variance: 6 / (3 - 1) = 3
For the small meal group:
Deviation from mean: (19 - 21) = -2, (23 - 21) = 2, (21 - 21) = 0
Squared deviations: (-2)^2 = 4, 2^2 = 4, 0^2 = 0
Sum of squared deviations: 4 + 4 + 0 = 8
Variance: 8 / (3 - 1) = 4
Finally, take the square root of the variance to get the standard deviation:
Standard deviation for the big meal group = sqrt(3) ≈ 1.732
Standard deviation for the small meal group = sqrt(4) = 2
Now that we have the mean and standard deviation for both groups, we can proceed to step 4 and determine the sample score on the comparison distribution.