Test 4 QRM

how to find z score

(x-mean)/standard deviation

4 advantages of z scores

-Mean is 0, makes it easy to interpret if a score is above or below it -SD is 1, makes it easy to tell how many SDs a score is in relation to the mean -Increased comparability of scores / Can easily combine or compare scores from distributions with different means and SDs -IF raw scores are normally distributed, z scores provide info about percentile rank

Limitations of percentile rank

-Ordinal -Does not provide information about how much lower or higher a score is

solving: z test for a single proportion

1. Find P value: proportion of sample: (sample x out of sample n) 2. Find Pi value: prop from general population 3. find the standard deviation of p 4. find Z 5. compare to z critical

What is the probability of selecting a random sample of n people with a sample mean of X or greater?

1. find standard error of the sample 2. find z score using standard error 3. use standard normal distribution table 4. 0.5 - (value from table)

two-tailed test

A hypothesis test in which rejection of the null hypothesis occurs for values of the test statistic in either tail of its sampling distribution. nondirectional

one-tailed test

A hypothesis test in which rejection of the null hypothesis occurs for values of the test statistic in one tail of its sampling distribution. directional

z test for a single proportion

Dr. Roberts was interested in whether runaway adolescents between 12 and 18 years of age are more likely to drop out of school than the general population of adolescents. In the general population of adolescents 12 to 18, 6% drop out of school. In a random sample of 90 runaway adolescents, 15 dropped out of school. Perform a statistical test to determine whether runaway adolescents are more likely to drop out of school than the general population of adolescents.

Major goals of inferential statistics

Hypothesis Testing Estimation -Point estimation -Interval estimation

Finding Z with standard deviation of Pi

P - Pi / STD of P

rejection region

Rejection region is the area under the normal curve where we reject the null hypothesis if the obtained value of the test statistic falls there Basically, if the absolute value of the obtained value is less than the absolute value of the critical value, we accept the null hypothesis If the absolute value of the obtained value is greater than the absolute value of the critical value, we reject the null hypothesis

Find standard deviation of p

Square root of Pi(1-Pi) / N

alternative hypothesis

The hypothesis that states there is a difference between two or more sets of data.

Central Limit Theorem

The theory that, as sample size increases, the distribution of sample means of size n, randomly selected, approaches a normal distribution. The mean of the sampling distribution of the mean is equal to the population mean The SD of the sampling distribution of mean (Standard error of the mean) is equal to population SD divided by square root of sample size Shape of the sampling distribution approximates the normal distribution as sample size increases, irrespective of whether the population has a normal distribution

how to find proportion from z score

Use standard normal distribution table add value to 0.5 if its x or more subtract the value from 0.5 if its x or less if its between, keep value

T Scores, SAT Scores, and IQ Scores can all be converted to

Z Scores

z test for a population mean

a hypothesis test that evaluates how far the observed sample mean deviates, in standard error units, from the hypothesized population mean

z critical value

a number on the z measurement scale that captures a specified tail area or central area

z-score

a type of standard score that tells us how many standard deviation units a given score is above or below the mean for that group

find z score using standard error

sample mean - population mean / standard error

standard error of the sample

standard dev / √n

null hypothesis

the hypothesis that there is no significant difference between specified populations, any observed difference being due to sampling or experimental error.