Which expression represents the factored form of 6x^{2}-13x-5?
1 answer:
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Answer:
i) a) Normality : We assume that the data follows approximately a normal distribution
ii) Random sample: The data comes from a random sample
iii) The sample size represent <10% of the population size
We assume that all the conditions are satisfied for this case.
b)
So on this case the 95% confidence interval would be given by (364621.22;522488.775)
c) We are confident at 95% that the true mean of foreclosed homes sold's are between (364621.22;522488.775)
d) Since the lower value for the 95% confidence interval is higher than 300000 we can conclude that yes differes significantly and the true mean is different from 300000 at 5% of significance.
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
population mean (variable of interest)
s=195381 represent the sample standard deviation
n=26 represent the sample size
Part a
We need some conditions:
a) Normality : We assume that the data follows approximately a normal distribution
b) Random sample: The data comes from a random sample
c) The sample size represent <10% of the population size
We assume that all the conditions are satisfied for this case.
Part b
The confidence interval for the mean is given by the following formula:
(1)
In order to calculate the critical value we need to find first the degrees of freedom, given by:
Since the Confidence is 0.95 or 95%, the value of and
, and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-T.INV(0.025,25)".And we see that
Now we have everything in order to replace into formula (1):
So on this case the 95% confidence interval would be given by (364621.22;522488.775)
Part c
We are confident at 95% that the true mean of foreclosed homes sold's are between (364621.22;522488.775)
Part d
Since the lower value for the 95% confidence interval is higher than 300000 we can conclude that yes differes significantly and the true mean is different from 300000 at 5% of significance.