Question 56 – 4.3.1 Statistical hypothesis testing (A-level only) - Questions

An environmental agency monitors air quality at 8 different urban locations using two different portable sensors, Alpha ( $A$ ) and Beta ( $B$ ). The particulate matter readings ( $μg/m3\mu g/m^3$ ) recorded at the same time are shown in the table below:

Location	L1	L2	L3	L4	L5	L6	L7	L8
Sensor Alpha ( $A$ )	45	32	58	21	15	60	10	25
Sensor Beta ( $B$ )	40	35	50	28	12	65	18	22

Calculate Spearman's rank correlation coefficient for these data.

Test, at the 5% level of significance, whether there is a positive correlation between the readings of the two sensors. State your hypotheses clearly.

Sensor Beta was later found to have a calibration error at Location L2; the reading should have been 40 instead of 35.

Without performing any further calculations, explain the procedure for finding Spearman’s rank correlation coefficient given this change.

Location	L1	L2	L3	L4	L5	L6	L7	L8
Sensor Alpha ( $A$ )	45	32	58	21	15	60	10	25
Sensor Beta ( $B$ )	40	35	50	28	12	65	18	22

Calculate Spearman's rank correlation coefficient for these data.

Test, at the 5% level of significance, whether there is a positive correlation between the readings of the two sensors. State your hypotheses clearly.

Sensor Beta was later found to have a calibration error at Location L2; the reading should have been 40 instead of 35.

Without performing any further calculations, explain the procedure for finding Spearman’s rank correlation coefficient given this change.

4.3.1 Statistical hypothesis testing (A-level only)

Question 55

4.3.1 Statistical hypothesis testing (A-level only)

Question 55

4.3.1 Statistical hypothesis testing (A-level only)

Question 55

4.3.1 Statistical hypothesis testing (A-level only) Questions

4.3.1 Statistical hypothesis testing (A-level only)

Question 55

4.3.1 Statistical hypothesis testing (A-level only) Questions