Hypothesis testing for the mean

Question 1

hypothesis testing method

Answer 1

uses data from a sample to decide whether or not a statement about a population should be accepted or not
- null hypothesis is tested with a sample and retained or rejected

Question 2

steps to hypothesis tests

Answer 2

1. state the null and alternative hypotheses
2. summarise data into suitable test statistics (check distribution)
3. assuming null is true, find p-value (probability that the observed statistic value could occur if the null model were correct - smaller = more statistically significant)
4. decide if the result is statistically significant based on p-value and report your conclusion in the context of the study
   If p is greater of equal to a, do not reject null
   If p-value is smaller than a, reject null

test statistic = (sample value - null value)/null error

Question 3

hypothesis testing assuming sigma is known (using z scores)

Answer 3

for large samples or when the population (assuming null) is normal

Z = (X bar - mew)/sigma/square root(n)

This is the test statistic. if its bigger than expected for a standard normal, reject H0

Question 4

one or two sided tests

Answer 4

one sided situation: dont use petrol additive if it doesn’t improve consumption
two sided: engine bolts can’t be too big or small

Question 5

two sided differ in that:

Answer 5

Ha has mew not equally rather than mew is bigger or smaller

p-value is doubled

Question 6

CI and two sided tests

Answer 6

if mew 0 is 90%, p value is greater 10%. if less, reject

Question 7

hypothesis testing when sigma is unknown (t distribution)

Answer 7

tn-1 = (x bar - mew 0)/s/square root (n)

reject null with p value between 0.01 and 0.025
do not reject if it is greater than 0.05

Question 8

as df increases, the t distribution…

Answer 8

gets close to the normal (100 is very close)

Question 9

can you find p values in excel?

Answer 9

yes