Lecture 4 - Hypothesis Testing (One sample t-Test)

Question 1

What are the most common types of statistical inference?

Answer 1

• Significance tests

- Confidence intervals

Question 2

The _____ the sample size = the smaller the variance

Answer 2

larger

Question 3

The smaller the variance, the more ______ the sample is

Answer 3

accurate

Question 4

T or F: If the original population is itself normally distributed then the sample means will be normally distributed for any size sample

Answer 4

True

Question 5

What is the purpose of the Central Limit Theorem ?

Answer 5

• It provides some reassurance when we are not certain whether observations are normally distributed
• Means of reasonable sized samples will have a distribution that is approximately normal
• Inference procedures based on the sample mean can therefore often use the normal distribution
• Care must be taken not to input no reality to the original observations

Question 6

What do we use to describe the variability of individual observations?

Answer 6

standard deviation

Question 7

What do we use to describe the variability of a sampling distribution ?

Answer 7

standard deviation of the sampling distribution of means (the standard error of the mean)

sem

Question 8

What is the formula for sem ?

Answer 8

sem = SD / square root (n)

Question 9

For ____ distributions, the mu +/- SD contains 68.26% of the observations

Answer 9

normal

Question 10

For _____ distributions, the mean +/- sem contains 68.26% of the observations

Answer 10

sampling

Question 11

As the sample means are normally distributed, we can define a ______ ______ (limits); a range of values used to estimate the true value of the population parameter

Answer 11

confidence interval

Question 12

For a 90% confidence interval, what is alpha ?

Answer 12

0.1

Question 13

For a 99% confidence interval, what is alpha ?

Answer 13

0.01

Question 14

For a 95% confidence interval, what is alpha ?

Answer 14

0.05

Question 15

What happens when we decrease alpha ?

Answer 15

increase our confidence but reduce our precision (widen the CI)

Question 16

How do you find 95% CI for for a sampling distribution?

Answer 16

x +/- 1.96(sem)

sem = SD/square root of n

Question 17

What are our assumptions for confidence intervals?

Answer 17

1) Random sampling - If the sample is biased our conclusions are not valid

2) Independent observations - If this assumption is violated, confidence intervals cannot be obtained.
ex. we do a pop quiz, other kids do a pop quiz later = independent
ex. we do a pop quiz on Tues and then do the same pop quiz on Thurs = not independent

3) Sampling from a normal population - We know that if the population is not normal, CI can still be obtained. From central limit theorem we know that if we have a large enough sample size we compensate for non-normal population.

Question 18

What is the formula for degrees of freedom?

Answer 18

df = n - 1

so 21 subjects would have a df of 20

Question 19

Describe the steps in hypothesis testing

Answer 19

1) State the null hypothesis: Any differences in the data are due to chance
2) State the alternative hypothesis: Any differences in the data are real or significant
3) Set the decision level, alpha: Hypothesis testing involves establishing P(H0 true). If this is very small we may reject H0. By convention, small means P < alpha with alpha=0.05
4) Choose the test statistic
5) Calculate P(H0 true): That is, assume H0 is true and calculate the probability of the outcome of the investigation being due to chance alone (due to random effects); we use an appropriate sampling distribution for this calculation
6) Make a decision concerning H0: It follows that if we reject H0 we are in a position to accept Ha as the logical alternative

P(H0 is true) < 0.05; reject H0

P(H0 is true) > 0.05; retain H0

Question 20

What way do you round degrees of freedom ?

Answer 20

Round down

Question 21

One sample t test, you are comparing it to the ____

Answer 21

mean

Question 22

Two sample t test, you are comparing them to ____ ____

Answer 22

each other