Hello,
I've lost my revision notes for an exam tomorrow (I know, I know!) and I was hoping someone could help me with the following:
1. deduce the population mean (u)
2. demonstrate how to carry out a hypothesis test at the 0.95 probability level as to whether population mean is greater than 80.
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This is for grouped data, and I have the following info:
n = 207
Arithmetic mean = 86.64
Median = 79.02
Standard deviation = 24.38
Co-efficient of variation = 28.14
Ql = 69.69
Qu = 102.92
Interquartile range = 86.31
Skewness = 0.94
sum of fx' = 17935
sum of fx'² = 1676975
Can anyone help??
Coefficient of variation=s/Xbar=0.2814 or 28.14%,
You did not mention percentages in you question, the default withou
qualification is a decimal fraction not a percentage. If you wish to give the
coefficient of variation as a percentage you have to say that is what it is.
RonL
Thank you, my mistake.
Regarding the population mean, I'm not very far into this but have the following:
H0 = u > 80
H1 = u (equal or less) 80
1.66 (1 sided 95% test)
Test statistic = 86.64 - 80 / SE = 3.9184972
where SE = 1.6945272 (24.38 / sqroot of 207)
Not quite sure where to go now with the test statistic...
Usual estimator of the population mean is the sample mean (though
caution is called for here as we have skewed data)
Here we have a large sample so we assume that the distribution of the2. demonstrate how to carry out a hypothesis test at the 0.95 probability level as to whether population mean is greater than 80.
sample means are normal with mean mu and SD sigma/sqrt(N), where mu is
the population mean, sigma the standard deviation of the population, and N
is the sample size. We also assume that we can use the standard deviation
s in place of the unknown population SD.
RonL
You will note that I have changed my post, as we dont want a 95%
confidence interval, but a one sided 95% test.
This is essentialy that the population mean should not be less than
86.64 - 1.645*s/sqrt(207) ~= 83.85,
where the 1.645 is the onesided 95% critical value for the standard normal
distribution.
RonL
My table gives 1.645, but it has been in error before, checking a second
source though confirms the 1.645.
The wording of these things is always tricky. I think that this is close enoughBUT in relation to the question, would this imply that it is "95% probable" that the population mean is greater than 80? Would that be a reasonable way to phrase the answer?
to be acceptable. A more carefull wording might be "There is a probability of
95% that the interval [83.85, infty) contains the population mean.
RonL
Thanks for your help with this.
I got through the exam ok and I think generally I answered the questions well. Not 100% confident about "deducing population mean u" as I didn't have the notes for that, but in terms of hypothesis testing I probably didn't drop many points.
Thanks again.
BTW 1.645 was indeed correct (my notes suggest otherwise unfortunately!)