Stat Formulas - Lecture notes 1-4 PDF

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Stat 208 Forumulas Notes ...

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STAT 208 (Elementary Statistics) – Page 1

Formula Sheet

Chapter 2 𝑎𝑏𝑠𝑜𝑙𝑢𝑡𝑒 𝑒𝑟𝑟𝑜𝑟/𝑐h𝑎𝑛𝑔𝑒/𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 = (claimed value) − (true value) 𝑟𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝑒𝑟𝑟𝑜𝑟/𝑐h𝑎𝑛𝑔𝑒/𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 = (absolute error) ×  1 00% (true value) 𝑖𝑛𝑑𝑒𝑥 𝑛𝑢𝑚𝑏𝑒𝑟 = 𝑣𝑎𝑙𝑢𝑒  × 100 𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑣𝑎𝑙𝑢𝑒 Chapter 4 1 . E squared Margin of error 95% confidence = 2x standard deviation Square root of N N = 267, sample mean of X is 77.0 grams and a standard deviation is 58.6 grams. Margin of error = (2 x 58.6) / (16.34) = 7.2 and the confidence interval is between 69.8 and 84.2 grams Population proportion = 

Chapter 7 Equation of a line:

𝑦 = 𝑚𝑥 + 𝑏 Chapter 5

Sample Means Population of 5, sample of n=1 5 samples. Sample of n=5 is all five in pop. 2 = 10 samples, 3 = 10 samples. Mean of distribution sample is the same as population mean.

Chapter 6 Probability (theoretical):

𝑃(𝐴) = # 𝑜𝑓 𝑤𝑎𝑦𝑠 𝐴 𝑐𝑎𝑛 𝑜𝑐𝑐𝑢𝑟 𝑡𝑜𝑡𝑎𝑙 # 𝑜𝑓 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠 Total # of outcomes

Probability (relative frequency): 𝑃(𝐴) = # 𝑜𝑓 𝑡𝑖𝑚𝑒𝑠 𝐴 𝑜𝑐𝑐𝑢𝑟𝑟𝑒𝑑 𝑡𝑜𝑡𝑎𝑙 # 𝑜𝑓 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛𝑠 Relative: frequency in category / total frequency Total # of observations Cumulative: category and all preceding 𝑃(𝐴) = 1 − 𝑃(𝐴) Joint probability (independent events): Joint probability (dependent events): “Or” probability:

𝑃(𝐴 𝑎𝑛𝑑 𝐵) = 𝑃(𝐴) × 𝑃(𝐵) 𝑃(𝐴 𝑎𝑛𝑑 𝐵) = 𝑃(𝐴) × 𝑃(𝐵 𝑔𝑖𝑣𝑒𝑛 𝐴) 𝑃(𝐴 𝑜𝑟 𝐵) = 𝑃(𝐴) + 𝑃(𝐵) − 𝑃(𝐴 𝑎𝑛𝑑 𝐵)

Probability Event Not Occurring Probability = P(A) event not occurring Not A is the complement of the event A.

P(A) + P(not A) = 1, or P(not A) = 1 - P(A) The not is designated by a bar, so Ā means not A.

To make a decimal from probability fractions: 2 coins tossed. 4 outcomes, but only 3 events. Out of four outcomes

(HH) (TT) and (HT) or (TH) are the same. (HH) is 1 out of 4. So ¼ = 0.25.

Same for TT. But for the other two, it’s one event but two separate outcomes. It would be 2/4 = 0.50.

MTH 157 (Elementary Statistics)

Formula Sheet – Page 2

Chapter 8 Standard Deviation - find mean of data set. Each deviation = (data value - mean) Standard deviation of distribution of sample means:

𝜎𝑥 = 𝜎 √𝑛

Standard deviation of distribution of sample proportions:

𝜎𝑝 = √𝑝(1−𝑝) 𝑛

Confidence interval (estimating a mean): Margin of error (estimating a mean): Expected Value Event Value

𝑥 ± 𝐸

Probability

𝐸rror = 2𝑠 √𝑛 Value x Probability (add column together)

Sample size (estimating a mean): 𝑛 = (2𝑠 / E) squared Confidence interval (estimating a proportion): 𝑝 ± 𝐸 Margin of error (estimating a proportion): 𝐸 = 2√𝑝(1−𝑝) 𝑛 Sample size (estimating a proportion): 𝑛=1 𝐸2 Chapter 9 Percent changes: subtract for difference, divide difference by original and x by 100 Find percent of a number: 15% = 0.15 x whatever number What percent of # is another #: divide A by B and move decimal 2 places to the right Probability of A = P(A) -- law of large numbers Ex. a roulette wheel has 38 numbers: 18 black, 18 red and the numbers 0 and 00 in green. P(red) = 18/38 = 0.474 = 47.4% of the time you’d get red, out of 100,000 = 47,400 Chapter 10 H0 (null hypothesis): μ = 62 miles per gallon Ha (alternative hypothesis): μ < 62 miles per gallon Statistical Significance of Hypothesis If it’s 0.01, it has strong evidence to reject original hypothesis, not the new one. If it’s 0.05, it has moderate evidence to reject. Standard Score of Sample Distribution

P-Value -- probability value (less than 0.05 rejects original/null hypothesis, greater than 0.05 does not reject) p -- population proportion p -- sample proportion x -- sample mean n = sample size

μ = population mean σ = population standard deviation...