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Q28Section A (Section A)28 of 60

Runs test for AQI signs

The recorded air quality index (AQI) at a place in a city for 1616 consecutive days for the current year is compared with the historical average AQI. The direction of the recorded AQI is noted as '++' if it is above the historical average and as '−-' if it is below the historical average. The dataset is as below: + + − + − − + + + + − − − + + −+\,+\,-\,+\,-\,-\,+\,+\,+\,+\,-\,-\,-\,+\,+\,- The total number of runs, RR, is being used to test H0H_{0}: The direction of the recorded AQI is random against H1H_{1}: The direction of the recorded AQI is not random. Consider the following statements. PP: The observed value of total number of runs is 88. QQ: Based on the above dataset, H0H_{0} is rejected in favor of H1H_{1} at level 0.050.05. Then which one of the following is true? [You may use: Under H0H_{0}, with 77 negative signs and 99 positive signs, P(R≤6)=0.108P(R\le 6)=0.108, P(R≤7)=0.231P(R\le 7)=0.231, P(R≤8)=0.427P(R\le 8)=0.427]

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