An engineer is testing the efficiency of a high-performance lithium-polymer battery pack for an industrial drone. During a controlled test flight, the engineer records the flight duration, TTT minutes, and the terminal voltage, VVV volts, of the battery pack. A random sample of 8 readings was taken during the first 40 minutes of flight, as shown in the table below:
| TTT (min) | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 |
|---|---|---|---|---|---|---|---|---|
| VVV (volts) | 12.35 | 12.12 | 11.85 | 11.60 | 11.38 | 11.10 | 10.88 | 10.60 |
You may use the following summary statistics:
∑T=180 \sum T = 180 ∑T=180 ∑V=91.88 \sum V = 91.88 ∑V=91.88 STT=1050 S_{TT} = 1050 STT=1050 SVV=2.6064 S_{VV} = 2.6064 SVV=2.6064 ∑TV=2015.0 \sum TV = 2015.0 ∑TV=2015.0Calculate the value of STVS_{TV}STV.
Find the equation of the regression line of VVV on TTT in the form V=a+bTV = a + bTV=a+bT. Give the values of aaa and bbb correct to 3 significant figures.
Use your equation to estimate the terminal voltage of the battery pack after 18 minutes of flight.
Comment on the reliability of your estimate in (c), giving a mathematical reason for your answer.
A specialized long-range mission requires the drone to fly for 90 minutes.
Give a reason why the equation in (b) should not be used to estimate the battery voltage for this mission.
355 exam-style questions on OCR (MEI) A Level Maths 2.5 Statistical Hypothesis Testing, covering 2.5.1 Process and language of hypothesis testing, 2.5.2 When to apply 1-tail and 2-tail tests, 2.5.3 Significance level and incorrect rejection, 2.5.4 Null and alternative hypotheses (binomial), 2.5.5 Conduct a binomial hypothesis test, 2.5.6 Critical and acceptance regions (binomial), 2.5.7 Distribution of the sample mean (A-level only), 2.5.8 Hypothesis test for a single mean (A-level only), 2.5.9 Critical and acceptance regions (mean) (A-level only), 2.5.10 Correlation as closeness to a straight line (A-level only), 2.5.11 Inference using a correlation coefficient (A-level only), and 2.5 Statistical Hypothesis Testing. Each one has a worked solution and a mark scheme showing where the marks go.