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Sample size calculator. Baseline conversion rate (control) % Confidence level % Statistical power % Conversion rate lift % % Number of variants. Required sample size ...

Hypothesis Testing for a Proportion and . for a Mean with Unknown Population Standard Deviation. Small Sample Hypothesis Tests For a Normal population. When we have a small sample from a normal population, we use the same method as a large sample except we use the t statistic instead of the z-statistic.

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You can use sample proportions to check out a claim about a population proportion. (This procedure is a hypothesis test for a population proportion.) In the ACT example, the probability that more than 45% of the students in a sample of 100 need math help (when you assumed 38% of the population needed math help) was found to be 0.0749.

Proportions • Let X ~ B(n, p) and is the sample proportion. • If n is large*, then • *Rule of Thumb: np ≥ 5, n(1 - p) ≥ 5. pXnˆ = / ˆ is approx. ( , (1 ) / ). is approx. ( , (1 ) ) p N p p -p n X N np np -p

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(b) Use the sample proportion pˆ as a p oint estimator for the population proportion p. The point estimate is pˆ 124 1473 == 0.084 . (c) Use the sample standard deviation s as a point estimator for the population standard deviation σ. The point estimate is s x =0.664 hour. EXAMPE L From batteries to smoking

Solution for Assume that a sample is used to estimate a population proportion p. Find the 99.5% confidence interval for a sample of size 329 with 58.1%…