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BSAN 202 Formulas Test Questions with Answers series of independent trials. success or failure. probability of success is constant - Answer-conditions for binomial distribution P(x) = (n choose x) pi^x (1 - pi)^(n - x). E(X) = n(pi). Var(X) = n(pi)(1 - pi) - Answer-Binomial probability formu...

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  • August 16, 2024
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  • 2024/2025
  • Exam (elaborations)
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BSAN 202 Formulas Test Questions
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series of independent trials. success or failure. probability of success is constant -
Answer-conditions for binomial distribution

P(x) = (n choose x) pi^x (1 - pi)^(n - x). E(X) = n(pi). Var(X) = n(pi)(1 - pi) - Answer-
Binomial probability formula: if the random variable x has a binomial distribution: ___. n=
sample size. pi= the probability of success for each trial.

n(pi) > 5. n(1 - pi) > 5 - Answer-Conditions to use the normal approximation to the
binomial:

X bar has an approximate normal distribution with mean = mu and standard deviation =
sigma x = sigma / sq rt(n) - Answer-Distribution of the sample mean: if a random sample
of size n is taken from a population with mean = mu and standard deviation = sigma,
then the sample mean of ___

T has an approximate normal distribution with mean = n(mu) and standard deviation
sigma t = (sq rt(n)) (sigma) - Answer-Distribution of sample sum: if a random sample of
size n is taken from a population with mean = mu and standard deviation = sigma, then
the sample sum of ___

X bar +/- (1.96 x sigma x bar). sigma x bar = sigma / sq rt(n) - Answer-Confidence
Interval for mean (known population standard deviation)

X bar +/- (t[n - 1, a/2] x S x bar). S x bar = s / sq rt(n) - Answer-confidence interval for
mean (unknown population standard deviation)

pi hat +/- (1.96) sq rt(pi hat x (1 - pi hat) / n) - Answer-confidence interval for pi

H null: mu = mu null vs Ha: mu does not = mu null. Test statistic: Z = x bar - mu null /
(sigma / sq rt(n)). reject H null if |Z| > 1.96 - Answer-hypothesis test for a mean with a
known standard deviation (sigma known)

test statistic: t = x bar - mu null / s x bar. S x bar = s / sq rt(n). Reject H null if |t| > t [n -
1, .025] df = n - 1 - Answer-test H null: mu = mu null vs Ha: mu does not = mu null.
population standard deviation unknown

test statistic: t = (x bar1 - x bar2) / sq rt((s1^2 / n1) + (s2^2 / n2)). Reject H null if |t| > t
[df, .025] df = n1 + n2 - 2 - Answer-test H null: mu1 - mu2 = 0 vs Ha: mu1 - mu2 does
not = 0.

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