math 105 chp 6 (a,b,c,d)

GPA

(credits worth * score)/ total attempted credits

outcomes of hypothesis test

1. rejecting the null hypothesis bc we have support of the alt. hypothesis (larger than 5%) 2. not rejecting the null hypothesis bc we lack support of the alt. hypothesis (smaller than 5%)

margin of error

1/ the square root of N. decreases as sample size increases.

symmetric distribution

A​ single-peaked distribution is symmetric if its left half is a mirror image of its right half.

mean

The mean is the sum of all the values divided by the number of values. It can be strongly affected by outliers.

median

The median is the middle value in a data set. It is not affected by outliers.

mode

The mode is the most common value in a data set. It is not affected by outliers.

quartiles of distibution

The quartiles are values that divide the data distribution into quarters.

standard deviation

a measure of how far data values are spread around the mean of a data set. the square root of the sum of deviations from the mean (squared) divided by the total number of data values minus 1.

outlier

a value that is much higher or much lower than almost all other values. can change the mean of a data​ set, but does not affect the median or mode.

null hypothesis

claims a specific value for a population parameter. ex. mean age = 15 years

sampling distribution

consists of proportions from many individual samples

deviation

data point - mean

upper quartile (3rd)

divides the loest three-fourths from a data set from the upper fourth. the median of the data values in the upper half of a data set.

lower quartile (1st)

divides the lowest fourth of a data set from the upper three-fourths. the median of the data values in the lower half of a data set.

95% confidence interval

found by subtracting and adding the margin of error from the sample proportion. you can be ___ ______ that the true population lies within this interval.

68-95-99.7 Rule

gives precise guidelines for the percentage of data values that lie within 1,2, and 3 standard deviations of the mean for any normal distribution.

statistically significant

it is unlikely to have occurred by chance. the results are substantial enough to reject the orginal hypothesis about the population and accept an alternative hypothesis.

five number summary

low value, lower quartile, median, upper quartile, high value.

left skewed

smaller on the left

right skewed

smaller on the right

range rule of thumb

standard deviation ≈ range / 4

normal distribution

symmetric, bell-shaped distribution with a single peak. Its peak corresponds to the​ mean, median, and mode of the distribution. Its variation is characterized by the standard deviation of the distribution.

alternative hypothesis

the claim that is accepted if the null hypothesis is rejected. ex. mean age < 15 years

range

the difference between the highest and lowest values

standard score

the number of standard deviations a data value lies above or below the mean.

middle quartile (2nd)

the overall median

estimating high value w/ rule of thumb

≈ mean + (2 x standard deviation)

estimating low value w/ rule of thumb

≈ mean - (2 x standard deviation)