Male: 60,63,65,70,66,80,85,73,79,80,83,85,81,76, 77,90,91,88,78,92
Females:
62,69,70,72,78,77,79,83,80,88,90,90,98,100, 66,67,65,63,69, 83
Can you hellp me I need to find:
A) P value and the Z value of this data with a Alpha Value of 0.05.
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To find the p-value and the z-value for the given data with an alpha value of 0.05, we need to follow these steps:
Step 1: Calculate the means of the male and female data.
For males:
Mean (x̄) = (60 + 63 + 65 + 70 + 66 + 80 + 85 + 73 + 79 + 80 + 83 + 85 + 81 + 76 + 77 + 90 + 91 + 88 + 78 + 92) / 20
= 1570 / 20
= 78.5
For females:
Mean (x̄) = (62 + 69 + 70 + 72 + 78 + 77 + 79 + 83 + 80 + 88 + 90 + 90 + 98 + 100 + 66 + 67 + 65 + 63 + 69 + 83) / 20
= 1609 / 20
= 80.45
Step 2: Calculate the standard deviation of the male and female data using the formula:
For males:
Standard Deviation (s) = sqrt(Σ(x - x̄)^2 / (n - 1))
= sqrt((60 - 78.5)^2 + (63 - 78.5)^2 + ... + (92 - 78.5)^2 / (20 - 1))
= sqrt(3845.5 / 19)
= sqrt(202.92)
≈ 14.25
For females:
Standard Deviation (s) = sqrt(Σ(x - x̄)^2 / (n - 1))
= sqrt((62 - 80.45)^2 + (69 - 80.45)^2 + ... + (83 - 80.45)^2 / (20 - 1))
= sqrt(3153.35 / 19)
= sqrt(165.91)
≈ 12.88
Step 3: Calculate the Z-value using the formula:
Z = (x̄1 - x̄2) / sqrt(s1^2 / n1 + s2^2 / n2)
= (78.5 - 80.45) / sqrt(14.25^2 / 20 + 12.88^2 / 20)
= -1.95 / sqrt(7.603 + 7.548)
≈ -1.95 / sqrt(15.151)
≈ -1.95 / 3.89
≈ -0.501
Step 4: Look up the Z-value in a Z-table to find the corresponding p-value.
A Z-table gives you the area under the standard normal curve to the left of a certain Z-value. To find the p-value, we need to find the area to the right of the Z-value.
Using a Z-table or a calculator, we find that the area to the left of -0.501 is approximately 0.3085. Therefore, the area to the right (p-value) is approximately 1 - 0.3085 = 0.6915.
So, the p-value for the given data is approximately 0.6915 and the z-value is approximately -0.501.