Question 1203088: 1) n= 10
2698, 2028, 2474, 2395, 2372, 2475, 1927, 3006, 2334, 2379,
i. point estimate of the population mean
The point estimate of the population mean is 2409
ii. 95% confidence interval for the population mean
confidence interval = z for 95% CI= 1.96
95% confidence interval = (i did a lot of these kind of questions already but i still wasn't sure whether to use t-statistics or z-statistics in a lot of those questions, so can you pls help explain? Also i dont understand how do i find the standard deviation)
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! you can use the descriptive sttistics calculator at https://www.calculatorsoup.com/calculators/statistics/descriptivestatistics.php to get your descriptive statistics for this data set.
here are the results from the use of that calcultor.
this is probably more than you need, but what you do need shoud be in there.
if they do not tell you that it is a sample from a larger population, then you should be able to assume that it is the population.
i don't see anything in what you provided that tells me that this is a sample, and not the population.
all i saw is that it was described as a data set.
if in doubt, ask your professor.
the rules for whether you should use the t-scoe or the z-score are summarized in the following reference.
https://www.statology.org/t-score-vs-z-score/
to find the variance, you ned to get the sum of squars.
that is the sum of the squared deviations from the mean.
for example, the men of your data set is 2408.8
you would subtract the mean from each data point in the data set and hen square it.
for example, your first data point is 2698.
you subtract the mean from this to get 2698 - 2408.8 = 289.2.
you square it to get 289.2^2 = 83636.64.
you do this for each data point in the data set.
then you take the sum of all the (data point minus mean) squared.
the result is the sum of squares.
that sum is 834085.6.
if your data set is the population, you divide
d that by the number of elements in the data set to get the variance.
you then take the square root of that vraiance to get the standard dviation.
if your data set is a sample, you divide that by 1 less than the number of data elements in the data set to get the variance.
you then take the square root of that variance to get the standad deviation.\
if your data set is the population, then you would use the z-core.
if your data set is a sample, then you would determine if you have the standard deviation from the population or the sample.
in his particular case, i'm assuming it's from the population so the z-score is the one to use.
if this is from a sample of the popula;tion, then you would not have been given the standard deviation of the population, so you would obtain the standard deviation from the data set and you would use the t-score rather than the z-score.
the t-score is derived the same way you derive the z-score, i.e. the formula is either z = (x - m) / s or t = (x - m) / s.
s is the standard error.
if you know the population standard deviation, then s = population standard deviation divided by square root of sample size and you would use the z-scdore.
if you don't know the population standard deviation and were either given the sample standard deviation or you derived the sample standaed deviation, then s = sample standard deviation divided by square root of sample size and you would use the t-score.
note that both of these assume you are dealing with a sample rather than the population.
it's still not clear to me whether you are dealing with a population or a sample.
you have to determinde that first.
without any additional information, i would assume population, but you should really verify with your professor if you can.
the 95% two tailed confidence interval for z-score is equal to plus or minus 1.95996.
the 95% two tailed confidence interval for t-score with 9 degrees of freedom (sample size minus 1) is equal to plus or minus 2.26216.
i think i answered your questions.
if not, let me know and i'll work harder to explain better.
i also did the sum of square calcultions in excel.
this is what the excel results look like.
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