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.
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??
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.
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...
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.
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
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.
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.
BTW 1.645 was indeed correct (my notes suggest otherwise unfortunately!)