a city council has 12 members. Five are democratss and seven are republicans. How many ways can a four member comitte be selecte
1 answer:
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Answer:
Third side of the triangle should be larger than 5.9 km, and smaller than 23.1 km
Step-by-step explanation:
Let's examine the two extreme cases for any possible triangle that has two known sides and one larger than the other one. The attached figure tries to represent those extreme cases.
In the first depicted case, the third side (shown in red) is barely larger than the difference between the known sides (shown in green). So for this case we have that the third side must be > 14.5 km - 8.6 km
that is : third side > 5.9 km
In the opposite case, when we place the two known sides (shown in green) almost opposite to each other, the measure of the third side is almost (but not quite) the addition of the known sides.
Then this third side is < 14,5 km + 8.6 km = 23.1 km
Conclusion:
5.9 km < third side <23.1 km
Answer:
a) Null hypothesis:
Alternative hypothesis:
b)
c)
If we compare the p value and the significance level given we see that
so we can conclude that we FAIL to reject the null hypothesis, and the the actual mean is not different from the value of 800.
d)
Since the confidence interval contains the value 800 this result agrees with the result obtained in the hypothesis test we fail to reject the null hypothesis that the true mean is 800
Step-by-step explanation:
Data given and notation
represent the mean for the sample
represent the standard deviation for the population
sample size
represent the value that we want to test
represent the significance level for the hypothesis test.
z would represent the statistic (variable of interest)
represent the p value for the test (variable of interest)
a) State the null and alternative hypotheses.
We need to conduct a hypothesis in order to determine if the true mean is different from 800 centistokes:
Null hypothesis:
Alternative hypothesis:
We know the population deviation, so for this case is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:
(1)
z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
b) Calculate the statistic
We can replace in formula (1) the info given like this:
c) Calculate the P-value
Since is a two tailed test the p value would be:
Conclusion
If we compare the p value and the significance level given we see that
so we can conclude that we FAIL to reject the null hypothesis, and the the actual mean is not different from the value of 800.
d) Confidence interval
The confidence interval for the mean is given by the following formula:
(1)
For the 95% confidence interval the value of and
, with that value we can find the quantile required for the interval in the normal standard distribution.
And replacing we got:
Since the confidence interval contains the value 800 this result agrees with the result obtained in the hypothesis test we fail to reject the null hypothesis that the true mean is 800