Statistics Exam 2 Note Sheet
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The P-value is an area, if the p-value is low the null must go, and the p-value separates the critical region from the values that do not lead to rejection of the null hypothesis.
Assume that 71% of offspring peas have green pods. Suppose we want to find the probability that when seven offspring peas are randomly selected, exactly two of them are green. What is wrong with using the multiplication rule to find the probability of getting two peas with green pods followed by five peas with yellow pods: (0.71)(0.71)(0.29)(0.29)(0.29)(0.29)
(0.29)=0.00103?
A: The probability obtained in this way is too low, since it only accounts for the permutation of getting two green followed by five yellow. There are many other permutations through which totals of two green and five yellow can be obtained. o
About 68.27% of the area is between z=-1 and z=1 (or within 1 standard deviation of the mean).
Q: Weights of adult human brains are normally distributed. Samples of weights of adult human brains, each of size n=15, are randomly collected and the sample means are found. Is it correct to
conclude that the sample means are found. Is it correct to conclude that the sample means cannot be treated as being from a normal distribution because the sample size is too small? Explain.
A: It is not correct. The sample means can be treated as being from a normal distribution because
the sample weights come from a population that is normally distributed.
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A continuous random variable has infinitely many values associated with measurements.
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Central Limit Theorem: For random samples of sufficiently large size, the sampling distribution of the sample mean is approximately normal with mean μ
and standard deviation σ
√
n
.
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Conditions:
Randomization: Data values must be sampled randomly.
Independence Assumption: The sampled values must be mutually independent.
10% Rule: The sample size is no more than 10% of the population.
Needs a large enough sample. Must be at least 30.
*If it is normally distributed, you don’t have to worry about sample
size.
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Z
α
:
α is the areaunder the curve .
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For binomial distribution equation: “j” = successes, “n” = number of trials, “p” = probability of success
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For a percentage better or worse than μ
.
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Calculator: (2
nd
VARS) -> normcdf
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For a percentile or areas covered
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Calculator: (2
nd
VARS) -> invnorm
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σ
X
¿¿
: Need to look for a sample of a certain size that is compared to the population mean.
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The samplemean X
¿
that we compare to our historical data μ
.
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σ
:
based on historical data
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Z-score: Tells us how many standard deviations above or below the mean is a particular value.
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Mean of 0 and standard deviation of 1
