Answer:
(8) The correct option is (3).
(2) The correct option is (1).
Step-by-step explanation:
(8)
The hypothesis can be defined as:
<em>H₀</em>: There is no difference between the two population means, i.e. <em>μ₁ </em>= <em>μ₂</em>.
<em>Hₐ</em>: There is a difference between the two population means, i.e. <em>μ₁ </em>≠ <em>μ₂</em>.
The decision rule of the test based on confidence interval is:
If the (1 - <em>α</em>) % confidence interval consists the null hypothesis value then the null hypothesis is not rejected. and vice-versa.
The 90% confidence interval for the paired difference between means is, (-3.31, 14.74).
The interval consists the null value, 0.
Thus, the null hypothesis was failed to be rejected.
<u>Conclusion:</u>
No significant difference exists between the average difference in scores and the differences were calculated as 0.
Thus, the correct option is (3).
(2)
A (1 - <em>α</em>) % confidence interval implies that there is (1 - <em>α</em>) % chance of the population parameter to be contained in this interval.
Or if 100 such intervals are constructed then (1 - <em>α</em>) of these intervals will consist the true parameter value.
The 99% confidence interval for the difference between means is, (-0.124, 13.85).
This interval implies that the true mean difference between the two populations lies in this interval with probability 0.99.
<u>Conclusion:</u>
We are 99% confident that the difference between the average age of all men and all women who play golf at the course is between -0.124 and 13.85.
Thus, the correct option is (1).
