We have a sample of 28 data points. The sample mean is 30.0 and the sample standard deviation is 2.40. The confidence level required is 98%. Then, we calculate α by:
The confidence interval for the population mean, given the sample mean μ and the sample standard deviation σ, can be calculated as:
Where n is the sample size, and Z is the z-score for 1 - α/2. Using the known values:
Where (from tables):
Finally, the interval at 98% confidence level is:
The relationship between x and y is represent as:
Since, the relationship is linear.
The standard form of equation of line is:
Consider any two set x and y values from the given relationship.
Let (-2, 10) and (-1,7.5)
The equation of the linear relationship between x and y is:
y = -2.5(x + 2) + 10
Now, to check that the point (9, -17.5) lies on the represented relationship between x and y
Substitute x = 9 and y = -17.5 in the equation y = -2.5(x + 2) + 10
y = -2.5(x + 2) + 10
-17.5 = -2.5(9 + 2) + 10
-17.5 = -2.5(11) + 10
-17.5 = -27.5 + 10
-17.5 = -17.5
Thus, LHS = RHS
Hence the point (9, -17.5) lie on the given linear relationship between x and y.
Answer: The point (9, -17.5) lie on the given linear relationship between x and y.
