The data to the right represent the top speed (in kilometers per hour) Of all the players (except goaltenders) in a certain socc
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You did not attach any picture to solve this problem. We cannot calculate for the value of A’ and D’ without the correct graph. However, I think I found the correct graph (see attached), please attach it next time.
So we are given that the figure is dilated by a factor of, meaning that all of its end points are multiplied by 2. By this rule, all we have to do is to simply multiply the initial coordinates of A and D by 2 to get A’ and D’, that is:
A’ = (-1 * 2, -1 * 2) = (-2, -2)
<span>D’ = (2 * 2, -1 * 2) = (4, -2)</span>
Answer:
Is plausible that the successive throws are independent
Step-by-step explanation:
1) Table with info given
The observed values are given by the following table
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First shot Made Second shot missed Total
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Made 152 33 185
Missed 37 8 45
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Total 189 41 230
2) Calculations and test
We are interested on check independence and for this we need to conduct a chi square test, the next step would be find the expected value:
Null hypothesis: Independence between two successive free throws
Alternative hypothesis: No Independence between two successive free throws
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First shot Made Second shot missed
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Made 189(185)/230=152.0217 41(185)/230=32.9783
Missed 189(45)/230=36.9783 41(45)/230=8.0217
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On this case all the expected values are higher than 5 and the sample size 230 is enough to apply the chi squared test.
3) Calculate the chi square statistic
The statistic for this case is given by:
Where O represent the observed values and E the expected values. Replacing the values that we got we have this
Now with the calculated value we can find the degrees of freedom
on this case r means the number of rows and c the number of columns.
Now we can calculate the p value
On this case the pvalue is a very large value and that indicates that we can fail to reject the null hypothesis of independence. So is plausible that the successive throws are independent.