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2 answers:
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Answer:
a. z=3.09. Yes, it can be concluded that the population mean is greater than 50.
b. z=1.24. No, it can not be concluded that the population mean is greater than 50.
c. z=2.22. Yes, it can be concluded that the population mean is greater than 50.
Step-by-step explanation:
We have a hypothesis test for the mean, with the hypothesis:
The sample size is n=55 and the population standard deviation is 6.
The significance level is 0.05.
We can calculate the standard error as:
For a significance level of 0.05, the critical value for z is zc=1.644. If the test statistic is bigger than 1.644, the null hypothesis is rejected.
a. If the sample mean is M=52.5, the test statistic is:
The null hypothesis is rejected, as z>zc and falls in the rejection region.
b. If the sample mean is M=51, the test statistic is:
The null hypothesis failed to be rejected, as z<zc and falls in the acceptance region.
c. If the sample mean is M=51.8, the test statistic is:
The null hypothesis is rejected, as z>zc and falls in the rejection region.
You know 1 is not a root because the sum of the coeffcients of the equation is 14, not zero.
It is fairly easy to try 3 by synthetic division (see attachment), which tells you that 3 is a root and the remaining quadratic factor is x²-3x-5. The quadratic formula tells you the roots of that factor are
... x = (-b±√(b²-4ac))/(2a) = (3±√29)/2
The appropriate choices are
... C. (3-√29)/2
... D. (3+√29)/2
... F. 3
_____
The quadratic formula tells you the solution to
... ax²+bx+c=0
is x = (-b±√(b²-4ac))/(2a)
We have a=1, b=-3, c=-5.
