Triangle PQR has vertices P(–2, 6), Q(–8, 4), and R(1, –2). It is translated according to the rule (x, y) → (x – 2, y – 16). Wha
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Answer:
The 95% confidence interval for the difference between means is (-2164.21, -299.13).
The lower limit on the confidence interval is -$2164.21.
The upper limit on the confidence interval is -$299.13.
Step-by-step explanation:
The sample data is:
Gender Mean Std. dev. n
Female 2577.75 1916.29 67
Male 3809.42 2379.47 33
We have to calculate a 95% confidence interval for the difference between means, with a T-model.
The sample 1, of size n1=67 has a mean of 2577.75 and a standard deviation of 1916.29.
The sample 2, of size n2=33 has a mean of 3809.42 and a standard deviation of 2379.47.
The difference between sample means is Md=-1231.67.
The estimated standard error of the difference between means is computed using the formula:
The t-value for a 95% confidence interval is t=1.96.
The margin of error (MOE) can be calculated as:
Then, the lower and upper bounds of the confidence interval are:
The 95% confidence interval for the difference between means is (-2164.21, -299.13).
General Idea:
The angles which occupy the same relative position at each intersection where a straight line crosses two others. If the two lines are parallel, the corresponding angles are equal.
The angles that are formed on opposite sides of the transversal and inside the two lines are alternate interior angles. The theorem says that when the lines are parallel, that the alternate interior angles are equal.
Applying the concept:
Angles PBC and BAD are congruent by the <u>Corresponding Angle Theorem</u>.
Angles ABC and BAT are congruent by the <u>Alternate Interior angle Theorem</u>.
