Ch 7 Confidence Interval & Hypothesis Testing for Mean

if measuring variable is categorical, use

proportion

if measuring variable is quantitative, use

mean

steps for hypothesis testing

1. form the hypothesis

2. data collection (n, x̅, s)

3. check conditions

4. test statistic

5. p-value

6. decision rule

7. conclusion & interpretation

what symbol do you use for the mean in hypothesis testing?

mu (μ)

check conditions for mean

normality (satisfy at least 1)

n ≥ 30

pop. dist. is normal

test statistic (t)

x̅ - μ / SE

SE

s / √n

interpretation of test statistic (t)

the sample mean is __ SE above/below from the H_o value.

p-value

probability that null hypothesis is true for the given sample

left-tail test for p-value in R

pt (t, df)

right-tail test for p-value in R

1-pt (t, df)

2-tail test for p-value in R

2*pt (t, df)

use negative t value so you don’t get value >1

decision rule

p-val < α (reject)

p-val > α (do not reject)

interpretation if reject H_o

“we have sufficient evidence to conclude the H_a.”

interpretation if do not reject H_o

“we do not have sufficient evidence to conclude the H_a.”

if n inc., what happens to SE, test statistic (t), and p-val?

SE dec., t inc., p-val. dec.

if sample mean and H_o have a large difference, there’s more evidence for…

H_a

confidence interval for mean formula

x̅ ± t* (SE)

ME

t* (SE)

how is t* different than z*?

t* changes everytime based on the df.

df (degrees of freedom)

n-1

how do you find t* in R?

qt( __ , df)

__ = boundary (less than 1)

confidence interval interpretation

“we have 95% confidence that the true mean __ is btwn LB & UB”

if n inc., what happens to SE, ME, & CI width?

SE dec., ME dec., CI narrower

if CL inc., what happens to t*, ME, & CI?

t* inc., ME inc., CI wider

if given ME, t*, & s/SE, how do you find n?

must use z* to find n, can’t use t* b/c you need df

formula to find n

(z* x s / ME)²

how to get interval in R when given data set

t.test ( data set$column name, conf.level = 0.__)

how to get subset in R w/ data set

any name ← subset(data set, data set$column name == __)

hypothesis test in R w/ data set

t.test(subset name$column name, mu = __, alt = “g”/”l”/”two-sided”)

g= greater (right-side test)

l = less (left-side test)

default alt. is two sided

a confidence interval is only needed for a…

two-sided test

do you need to input the mu and alt. for a confidence interval in R?

no. only conf.level