Psych 300A: Final Review (Single Sample t Tests)

What is the major problem regarding z scores for hypothesis testing

We need to known the population parameters to participate in hypothesis testing which is often not known

How can we estimate mu and sigma

Mu - estimate using the sample mean, poses no additional problems

Sigma - estimate using the s of the sample, leads to sigma being underestimated

How do we calculate s

Same way as SD but replace N with N - 1 for the denominator

Degrees of freedom

Number of scores in a sample that are independent and free to vary

df = N - 1 in a single sample design

Estimated standard error

Used to estimate the population standard error when the value of sigma when sigma is not known

𝑠x̄ = s / √N

t statistic

Statistic used to test hypotheses about a population mean whent eh value of sigma is unknown

Calculated the same way as z but swap out the denominator with 𝑠x̄

How is t represented theoretically

(mean) - (mean of sampling distribution) / (estimated standard error)

(explained variability) / (unexplained variability)

What 2 conditions must be met to use a t test

1. We have scores for one sample of individuals

2. We want to compare this sample with a population where SD is unknown

T or F: When we estimate z from t they are always equal

F, not necessarily equal

T or F: The greater the degrees of freedom the better the s and sx represent the population and distribution statistics

T, also leads to the t distribution being more closely approximated to SND