a few stats qs

G

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Given the following sample, estimate the population variance with 98% confidence.
5 9 6 8 7 4 5 8

The answer is (1.1, 13.5), but does anyone know which formulas they used :oops: ?


Also:
Can we conclude at the 5% significance level that the population variance is greater than 25 if a random sample of 50 yields s2=30? Determine the test statistic needed to conduct the test of hypothesis.

the answer is c2 = 58.8 but does anyone how they got that?


Also:
A random sample of 12 observations was drawn from a large, normally distributed population. They are 12 18 21 16 32 28 19 11 22 26 15 13. What test statistic would you use to test at the 5% significance level whether the mean differs from 19?

why is it t=.2191 and not t=2.201?


Also:
A random sample of 12 observations was drawn from a large, normally distributed population. They are 12 18 21 16 32 28 19 11 22 26 15 13. Estimate the population mean with 90% confidence.

so u need to use t distribution because the population standard deviation is unknown, but which formula?


Also:
A biologist wants to estimate the proportion of trout in a certain lake. A sample of 50 fish contains 22 trout. Estimate the population proportion of trout with 90% confidence.
So the answer is (.32, .56), but which formula?
 
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