One hundred voters were asked their opinions of two candidates, a and b, running for mayor. their responses to three questions a
1 answer:
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Answer:
A: C = 2: 1
Step-by-step explanation:
Please see the attached pictures for the full solution.
Further explanantion (2nd image):
The reason why the ratio of A: C is equal to the ratio if 2A: 2C is that the number of parts of A and C is equal, which is 2 parts. If I were to divide both 2A and 2C by 2 to find the ratio of A: C, I would obtain 15: 15/2. However, ratios are expressed as whole numbers and thus, we would multiply the whole ratio by 2 again and the answer would still be 30: 15. This ratio is not in the simplest form since both can be divided by 15. Thus, dividing both sides of the ratio by 15 will leave us with the final answer of
A: C= 2: 1.
☆ An alternative method is to simplify the ratio 3B: 2C at the beginning.
3B: 2C
= 36: 15
= 12: 5
Multiply the first ratio by 2 so 3B has 12 parts in both ratios:
2A: 3B
= 10: 12
Combining the 2 ratios together,
2A: 3B: 2C
= 10: 6: 5
2A: 2C
= 10: 5
= 2: 1
A: C= 2: 1
Answer:
So on this case the 90% confidence interval would be given by
For this case since the confidence interval for the difference of means contains the 0 we can conclude that we don't have significant differences at 10% of significance between the two means analyzed.
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
represent the sample mean 1
represent the sample mean 2
n1=15 represent the sample 1 size
n2=15 represent the sample 2 size
population sample deviation for sample 1
population sample deviation for sample 2
parameter of interest at 0.1 of significance so the confidence would be 0.9 or 90%
We want to test:
H0:
H1:
And we can do this using the confidence interval for the difference of means.
Solution to the problem
The confidence interval for the difference of means is given by the following formula:
(1)
The point of estimate for is just given by:
The degrees of freedom are given by:
Since the Confidence is 0.90 or 90%, the value of and
, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.05,28)".And we see that
Now we have everything in order to replace into formula (1):
So on this case the 90% confidence interval would be given by
For this case since the confidence interval for the difference of means contains the 0 we can conclude that we don't have significant differences at 10% of significance between the two means analyzed.