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Answer:
a) The proportions are not form matched-pairs data.
b) The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that there is evidence of a significant increase in the proportion of people who suffer heart attacks when using Avandia compared to other treatments.
Step-by-step explanation:
a) Two data sets are "paired" when the following one-to-one relationship exists between values in the two data sets:
- Each data set has the same number of data points.
- Each data point in one data set is related to one, and only one, data point in the other data set.
None of this conditions apply in this case, so the proportions are not form matched-pairs data.
b) This is a hypothesis test for the difference between proportions.
The claim is that there is evidence to suggest that there is a significant increase in the proportion of people who suffer heart attacks when using Avandia compared to other treatments.
Then, the null and alternative hypothesis are:
The significance level is 0.05.
The sample 1 (Avindia treatment), of size n1=1456 has a proportion of p1=0.0185.
The sample 2 (other treatment), of size n2=2895 has a proportion of p2=0.0142.
The difference between proportions is (p1-p2)=0.0044.
The pooled proportion, needed to calculate the standard error, is:
The estimated standard error of the difference between means is computed using the formula:
Then, we can calculate the z-statistic as:
This test is a right-tailed test, so the P-value for this test is calculated as (using a z-table):
As the P-value (0.1358) is bigger than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that there is evidence to suggest that there is a significant increase in the proportion of people who suffer heart attacks when using Avandia compared to other treatments.
Answer:
- 14π/9; 108°; -√2/2; √2/2
Step-by-step explanation:
To convert from degrees to radians, use the unit multiplier
In equation form that will look like this:
- 280° ×
Cross canceling out the degrees gives you only radians left, and simplifying the fraction to its simplest form we have
The second question uses the same unit multiplier, but this time the degrees are in the numerator since we want to cancel out the radians. That equation looks like this:
×
Simplifying all of that and canceling out the radians gives you 108°.
The third one requires the reference angle of .
If you use the same method as above, we find that that angle in degrees is 135°. That angle is in QII and has a reference angle of 45 degrees. The Pythagorean triple for a 45-45-90 is (1, 1, √2). But the first "1" there is negative because x is negative in QII. So the cosine of this angle, side adjacent over hypotenuse, is
which rationalizes to
The sin of that angle is the side opposite the reference angle, 1, over the hypotenuse of the square root of 2 is, rationalized,
And you're done!!!