Please help me with both of these questions. THANK YOU in advance for your for you help.
13. For the data,
9 5 10 7 9 10 11 8 12 7 6 9
(a) Compute the z-score for the raw score of 10. (b) Compute the z-score for the raw score of 6.
14. For the data in question 13, find find the raw scores that correspond to the following:
(a) z = 11.22; (b) z = -0.48.
13. Find the mean first = sum of scores/number of scores
Subtract each of the scores from the mean and square each difference. Find the sum of these squares. Divide that by the number of scores to get variance.
Standard deviation = square root of variance
Z = (score-mean)/SD
13. Insert the Z score and other data to find the raw scores.
I'll let you do the calculations.
Sure, I'd be happy to help you with those questions!
13. To compute the z-score for a raw score, you need to know the mean and the standard deviation of the data set. Let's first calculate the mean and standard deviation for the given data set:
Data: 9 5 10 7 9 10 11 8 12 7 6 9
Mean (x̄) = (9+5+10+7+9+10+11+8+12+7+6+9)/12 = 95/12 ≈ 7.92
Next, we'll calculate the standard deviation (s). I'll walk you through the steps using the formula for sample standard deviation:
1. Calculate the squared difference between each data point and the mean:
(9-7.92)^2, (5-7.92)^2, (10-7.92)^2, (7-7.92)^2, (9-7.92)^2, (10-7.92)^2, (11-7.92)^2, (8-7.92)^2, (12-7.92)^2, (7-7.92)^2, (6-7.92)^2, (9-7.92)^2
2. Sum up all these squared differences:
(1.08)^2 + (2.92)^2 + (2.08)^2 + (0.92)^2 + (1.08)^2 + (2.08)^2 + (3.08)^2 + (0.08)^2 + (4.08)^2 + (0.08)^2 + (1.92)^2 + (1.08)^2 = 45.68
3. Divide the sum by (n-1), where n is the number of data points (12 in this case):
45.68 / (12-1) = 45.68 / 11 ≈ 4.15
4. Take the square root to find the standard deviation:
√4.15 ≈ 2.04
Now we have the mean (7.92) and the standard deviation (2.04). We can use these values to compute the z-scores:
(a) To compute the z-score for the raw score of 10:
z = (x - x̄) / s
z = (10 - 7.92) / 2.04
z ≈ 1.02
(b) To compute the z-score for the raw score of 6:
z = (x - x̄) / s
z = (6 - 7.92) / 2.04
z ≈ -0.94
14. To find the raw scores that correspond to given z-scores, we'll use the formula for z-scores:
z = (x - x̄) / s
Now, rearranging the formula, we can solve for x:
x = z * s + x̄
(a) For z = 11.22:
x = 11.22 * 2.04 + 7.92
x ≈ 30.78
(b) For z = -0.48:
x = -0.48 * 2.04 + 7.92
x ≈ 7.00
So, the raw score corresponding to z = 11.22 is approximately 30.78, and the raw score corresponding to z = -0.48 is approximately 7.00.
I hope this explanation helps! Let me know if you have any further questions.