7: Hypothesis Testing Flashcards
What does the symbol ‘H0’ represent?
(subscript zero)
H0 is the null hypothesis, a speculated assumption or a statement to be tested.
What does the symbol ‘H1’ represent?
(subscript 1)
H1 is the alternative hypothesis, the exact opposite of the null hypothesis.
Based on a statistical investigation, what are the two possible outcomes of hypothesis testing?
Reject H0 and adopt H1
OR
Conclude that there is no evidence to reject H0
What is a type 1 error?
We reject the null hypothesis when it is true
What is a type 2 error?
The null hypothesis is not rejected when it is false
What is the significance level?
The probability ‘alpha’ of making a type 1 error
What is the process for the one sample z-test for population mean? (7 steps)
1 - Define null hypothesis (H0)
2 - Define alternative hypothesis (H1)
3 - Define significance level (normally 1 or 5%)
4 - Determine rejection region using z-table
5 - Calculate the value of the test statistic (z)
6 - Compare test statistic to rejection region
7 - Formulate written conclusion
How is the written conclusion normally formatted if the test statistic falls within the rejection region?
The null hypothesis is rejected and the alternative hypothesis is adopted. There is evidence to suggest a significant difference between the sample mean and the hypothesised population mean.
what is ‘x squiggly line’?
Sample mean
What is ‘mu 0’?
Assessed population mean, comes from H0
what is ‘sigma’?
Known or previously estimated population standard deviation
What is ‘n’?
Sample size
How would you formulate the null hypothesis (H0) for the below scenario?
What would the formula be?
‘A local authority has introduced a car sharing scheme and has provided car parking data for the last two years prior to the scheme, and for 75 days subsequent to implementing the scheme.’
H0 = the average number of cars remains the same or has not decreased. In other words, the scheme does not work.
Sigma = Sigma 0 (i.e. no change)
How would you formulate the alternative hypothesis (H1) for the below scenario?
What would the formula be?
‘A local authority has introduced a car sharing scheme and has provided car parking data for the last two years prior to the scheme, and for 75 days subsequent to implementing the scheme.’
H1 = the average number of cars, population mean, has decreased. In other words, the scheme does work.
Mu < Mu 0 (i.e. population mean has decreased)
How do you convert the significance level (alpha) from % to decimal?
Divide by 100
What are the three forms of hypothesis testing and the equivalent formulas?
two-tailed test: Mu ≠ Mu 0 (not equal to)
left-tailed test: Mu < Mu 0 (less than)
right-tailed test: Mu > Mu 0 (greater than)
Where is the rejection area for the two-tailed test?
How is alpha converted?
At both the left and rightmost extents.
alpha/2, it is negative on the left and positive on the right.
Where is the rejection area for the left-tailed test?
How is alpha converted?
At the leftmost extent.
Alpha is negative.
Where is the rejection area for the right-tailed test?
How is alpha converted?
At the rightmost extent.
Alpha is positive.
How do you find the corresponding Z value on the Z table?
1 - Significance level (decimal), then find the value in the body of the table and read off the corresponding row and column values.
How do you find the corresponding Z value if the number is between two columns?
For example, 1.64 and 1.65
Add both columns together and divide by 2 (average them).
(1.64+1.65/2)=1.645
Propose a conclusion to the following scenario:
The test statistic, Z, has fallen within the rejection region for the below:
H0 - Car sharing scheme has not worked
H1 - Car sharing scheme has worked
5% occurrence
The alternative hypothesis is adopted: there is significant statistical evidence that the population mean (average number of parked cars per day) has reduced, because the sample mean falls within the region associated with just 5% occurrence.
What formula do you use for hypothesis testing for a significant difference between two sample means?
The ‘Z calc’ formula
What are the two hypothesis options for two sample mean hypothesis testing?
H0: (sigma 1 - sigma 2) = 0 (no significant diff.)
H1: (sigma 1 - sigma 2) ≠ 0 (significant diff.)
In hypothesis testing with two sample means, what do the subscripts 1 and 2 refer to?
1 relates to the first sample and it’s assumed population and 2 relates to the second sample and it’s assumed population.
What type of test are two sample means tests typically?
Two-tailed tests
What is the rejection region for a two-tailed test?
- Z value < x > + Z value
If no data exists for sigma 1 and/or sigma 2 (population standard deviation) what formula must be used to estimate this?
sigma est 1 = s1 * Sqr Root (n1/n1-1)
and the same for 2 with the second population values in place.
How do you phrase the acceptance of the null hypothesis in a multi population mean question?
There is not sufficient evidence to suggest the two samples have come from different populations, so the conclusion is that they come from the same population.
How do you phrase the rejection of the null hypothesis in a multi population mean question?
There is significant evidence to suggest that the samples have come from different populations.
