Topic B2 Hypothesis tests For each test remember to state the hypotheses formally, obtain the test statistic and critical value and state your conclusion in terms of the business problem.
Initially use a significance level (alpha) of 0.05 unless told otherwise
Q1. Test for Mean.
For each particulate PM10 and PM2.5 carry out a t-test using the null hypothesis that the mean concentration = 6 μg/m3.
For each t-test determine the p-value and comment on its meaning.
Note that this is TWO separate t-tests each for a single mean. [Another use of the t-test is to compare two means but you are not asked to do this here].
There will be TWO means and TWO standard deviations.
This is similar to some examples in the notes. You should comment on the validity of the test – revise the assumptions required for the t-test.
Our null hypothesis is that the mean is equal to a specific value: “using the null hypothesis that the mean concentration = 6 μg/m3.”
The alternate hypothesis is that it is NOT 6, so we could reject the null in EITHER direction (The actual figure could be higher or lower than 6).
This makes it a TWO tail test.
Be critical and question it by all means but still carry out the test!
Q2. Test for association.
Carry out a chi-squared test to determine whether the level of concentration of PM10 is independent of the region of the city. (20 marks)
Determine the p-value and comment on its meaning.
Your are given the data in the form of a two-dimensional frequency table (rows and columns).
These are the observed values. You need to calculate expected values. This is similar to examples in the notes but be careful as the size and shape of the tables is different.
Once you have both the observed and expected values you can use CHISQ.TEST to obtain the p-value directly.
Topic B3 Correlation and Regression
Calculated values for SLOPE, INTERCEPT and R2 using Excel functions should match those on the Scatter Graph (apart from rounding).
It is important to comment on any apparent relationship and whether it may be significant. The above calculations will NOT be able to tell you how significant it is, so initially make an intuitive judgement.
[p-value IS NOT REQUIRED FOR THE EXERCISE, but obtain it if you wish:
For a measure of significance you would need the p-value which can be obtained using the Data Analysis – Regression add-in feature.
