Independent random samples are taken at a university to compare the average GPA of seniors to the average GPA of sophomores. Giv
1 answer:
Answer:
Correct options is (A).
Step-by-step explanation:
A (1 - <em>α</em>)% confidence interval can be constructed to determine whether there is any difference between the average GPA of seniors and the average GPA of sophomores.
The hypothesis can be defined as:
<em>H₀</em>: There is no difference between the average GPA of seniors and the average GPA of sophomores, i.e. <em>μ</em>₁ - <em>μ</em>₂ = 0.
<em>Hₐ</em>: There is a difference between the average GPA of seniors and the average GPA of sophomores, i.e. <em>μ</em>₁ - <em>μ</em>₂ ≠ 0.
The (1 - <em>α</em>)% confidence interval for the difference between two means is:
Decision rule:
If the confidence interval contains the mull value, i.e. 0, then the null hypothesis will be failed to be rejected and vice-versa.
The 95% confidence interval for the difference between the true average GPAs (seniors - sophomores) is (0.53, 1.61).
The 95% confidence interval dos not contains 0. Thus, the null hypothesis will be rejected.
Conclusion:
There is a significant difference between the average GPA of seniors and the average GPA of sophomores.
The 95% confidence interval for the difference between the true average GPAs (0.53, 1.61), implies that there is a 95% confidence that the average GPA of seniors is greater than the average GPA of sophomores.
Thus, the correct options is (A).
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Answer: The correct option are as follows;
(1) The triangles are similar because corresponding sides are congruent
(2) The triangles are similar because alternate interior angles are congruent
(3) In the similar triangles, Angle 3 and Angle 6 are corresponding angles
Step-by-step explanation: Please refer to the picture attached for details.
The line i and line e has been drawn and marked as parallel lines. Also two transversal lines m and n have been drawn to intersect in the region between the parallel lines to form two triangles (as shown in the picture).
From the information given, where line e intersects with line n we have angle 1, and where line e intersects with line m we have angle 3, and then the third angle is angle 2.
Furthermore, where line l intersects line m we have angle 6, and where line l intersects line n is angle 4. Also in this second triangle, the third angle is 5.
Upon close observation we would see that Angle 6 is equal to Angle 3, since the transversal m has cut across both parallel lines l and e. Similarly Angle 4 is equal to Angle 1 since the transversal n has cut across parallel lines l and e. Having that Angles 3 and 1 are congruent to Angles 6 and 4, we can conclude that the value of the third angle in one triangle is equal to the that of the third in the second triangle, that is, Angle 2 equals Angle 5. Also, if the angles are similar and the lines l and e are parallel, then the lines formed in both triangles are equal.
So our conclusions are;
The interior angle are alternate angles (Angles 3 and 6, Angles 1 and 4), and the third interior angles are Opposite (Angles 2 and 5 {Opposite angles are equal})
Step-by-step explanation:
I am not sure about the answer of (b). Hope it helps :)
