Consider the following data drawn independently from normally
distributed populations: (You may find it useful to
reference the appropriate table: z table
or t table)
x−1x−1 = 28.5 | x−2x−2 = 29.8 |
σ_{1}^{2} = 96.9 | σ_{2}^{2} = 87.0 |
n_{1} = 29 | n_{2} = 25 |
a. Construct the 99% confidence interval for the
difference between the population means.
(Negative values should be indicated by a
minus sign. Round all intermediate calculations to at least 4
decimal places and final answers to 2 decimal
places.)
b. Specify the competing hypotheses in order to
determine whether or not the population means differ.
H_{0}: μ_{1} − μ_{2} = 0; H_{A}: μ_{1} − μ_{2} ≠ 0
H_{0}: μ_{1} − μ_{2} ≥ 0; H_{A}: μ_{1} − μ_{2} < 0
H_{0}: μ_{1} − μ_{2} ≤ 0; H_{A}: μ_{1} − μ_{2} > 0
c. Using the confidence interval from part a, can
you reject the null hypothesis?
Yes, since the confidence interval does not include the hypothesized value of 0.
No, since the confidence interval includes the hypothesized value of 0.
Yes, since the confidence interval includes the hypothesized value of 0.
No, since the confidence interval does not include the hypothesized value of 0.
d. Interpret the results at αα = 0.01.
We conclude that the population means differ.
We cannot conclude that the population means differ.
We conclude that population mean 2 is greater than population mean 1.
We cannot conclude that population mean 2 is greater than population mean 1.
Part a)
Confidence interval :-
Critical value Z(α/2) = Z (0.01 /2) = 2.576 ( From Z table )
Lower Limit =
Lower Limit = -8.03
Upper Limit =
Upper Limit = 5.43
99% Confidence interval is ( -8.03 , 5.43 )
Part b)
H_{0}: μ_{1} − μ_{2} = 0; H_{A}: μ_{1} − μ_{2} ≠ 0
Part c)
No, since the confidence interval includes the hypothesized value of 0.
Part d)
We cannot conclude that the population means differ.
Get Answers For Free
Most questions answered within 1 hours.