How do you solve system of eqautions using substitution
1 answer:
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Answer:
Null hypothesis:
Alternative hypothesis:
The p value is a very low value and using any significance level for example always
so we can conclude that we have enough evidence to reject the null hypothesis, and we can say the the proportion of Canadians is not significantly higher than the porportions of readers at Britons.
Step-by-step explanation:
1) Data given and notation
represent the number of Canadians randomly sampled by Gallup that read at least one book in the past year
represent the number of Britons randomly sampled that read at least one book in the past year
sample of Gallup selected
sample of Britons selected
represent the proportion of Canadians randomly sampled by Gallup that read at least one book in the past year
represent the proportion of Britons randomly sampled that read at least one book in the past year
z would represent the statistic (variable of interest)
represent the value for the test (variable of interest)
2) Concepts and formulas to use
We need to conduct a hypothesis in order to check if the proportion for men with red/green color blindness is a higher than the rate for women , the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
We need to apply a z test to compare proportions, and the statistic is given by:
(1)
Where
3) Calculate the statistic
Replacing in formula (1) the values obtained we got this:
4) Statistical decision
For this case we don't have a significance level provided , but we can calculate the p value for this test.
Since is a one side test the p value would be:
So the p value is a very low value and using any significance level for example always
so we can conclude that we have enough evidence to reject the null hypothesis, and we can say the the proportion of Canadians is not significantly higher than the porportions of readers at Britons.
Purple color figure is similar to the original figure.
<u>Solution:</u>
Property of similar polygon:
<em>Similar polygons have same shape, corresponding angles are congruent and the corresponding sides are in the same ratio.</em>
(1) <u>Compare original figure with green color figure:</u>
Angles of the original figure:
37°, 53° and 90°.
Angles of the green color figure:
67°, 23° and 90°
These two angles of the triangles not congruent angles.
Hence these shapes are not similar.
(2) <u>Compare original figure with yellow color figure:</u>
Angles of the original figure:
37°, 53° and 90°.
Angles of the yellow color figure:
67°, 23° and 90°
These two angles of the triangles are not congruent angles.
Hence these shapes are not similar.
(3) <u>Compare original figure with purple color figure:</u>
Angles of the original figure:
37°, 53° and 90°
Angles of the purple color figure:
37°, 53° and 90°
These two triangles have same shape and congruent angles.
Ratio of the sides:
These two triangles have same ratio.
Hence these shapes are similar.
Hence purple color figure is similar to the original figure.