11. Inference for a Normal Population

Question 1

If Y bar is normally distributed

Answer 1

we can convert it’s distribution to a standard normal distribution, giving the probability distribution of the diff. btwn a sample mean and the population mean

Question 2

formula for estimated standard error of the mean/standard deviation

Answer 2

SE[Ybar] = 2/ sqrt(n)

Question 3

test statistic t formula

Answer 3

{ Y bar - u } / [ s/sqrt(n) ]

Question 4

difference btwn Z and t formula

Answer 4

Both have a regular bell shaped curve

More pronouned differences in tail

In case of Z, denominator is alpha???, in t denom is estimate of Standard error of the mean

Question 5

using t-distribution to calculate a confidence interval of the mean

Answer 5

Y bar +/1 SE[Ybar] * talpha(2),df

talpha(2),df is found in t table

Question 6

alpha =

Answer 6

1 - confidence interval

alpha(2) indicates a two-tailed alpha, critical value that marks of 1/2 of alpha in upper and 1/2 in lower

Question 7

LOOK AT R FORMULAS IN SLIDE DECK

Question 7

when does t distribution become close to standard normal?

Answer 7

as degrees of freedom go up, t dist. converges on standard normal thus if you have LOTS of data, close to standard normal distribution

Question 8

conf interval about population variance formula

Answer 8

[df * s^2] / (chi-squared for alpha/2, df) </= sigma^2 </= [df * s^2] / (chi-squared for 1- alpha/2, df)

NOT a symmetrical distribution therefore needs to separate numbers from chi-squared table

Question 9

one sample t-test

Answer 9

compares the mean of a random sample from a normal population with the population mean proposed in a null hypothesis

Question 10

equation for t used in t-test

Answer 10

t = [Ybar - u0] / [s/sqrt(n)]

Question 10

Assumptions of t test

Answer 10

1. The variable is normally distributed
   * as long as sample is reasonably large and dist of mean is normally distributed, can still get relatively correct answer
2. The sample is a random sample

Question 11

summary of 1 sample t test

Answer 11

Compares a sample mean to a population mean proposed in a null hypothesis

Number of variables: 1
Type of variables: continuous numerical
Null hypothesis: u = u0
Test statistic: t
Degrees of freedom: n - 1
Assumptions: variable is normally distributed; random samplining