Chi Squared test

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A mathematics test of 100 multiple- choice questions is to be given to all freshmen entering a large university. Initially, in a pilot study the test was given to a random sample of 20 freshmen. Suppose that, for the population of all entering freshmen, the distribution of the number of correct answers would be normal with a variance of 250.
a. What is the probability that the sample variance would be less than 100?
b. What is the probability that the sample variance would be more than 500?

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@raghav674,

Why are you looking to do a chi square on normally distributed data?

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@raghav674,

a) 19*100/250 = 7.6 (see chi table) = P(s^2<100) = (1 - p = 1 - .99) = .01
b) 19*500/250 = 38 (see chi table) = P(s^2>500) = (1 - p = 1 - .995) = .005

to answer the other guy about normal distribution:
"The chi-square distribution and the resulting computed probabilities for various values of s^2 require that the population distribution be normal."
Statistics - Newbold, 7th edition, pg. 272

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@rdalt131,

to @raghav674,
you write see chi table (consider the second question b)==> I look into the table and try to find the 38 value? I found many: 37.916 (almost 38, for alpha 0.10), 38.885 (for the alhap=0.05) and 38.932 (for alpha0.01) so which one is the right one? and what the df=19 has to do here?
Thank you in advance

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Chi Squared test

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