An electrical engineer is comparing the charging times of heavy-duty capacitors from two different manufacturers, Manufacturer P and Manufacturer Q. Random samples of 75 capacitors from Manufacturer P and 80 capacitors from Manufacturer Q are tested, and the charging time, ttt minutes, of each capacitor is recorded.
The table below summarizes the data:
| Manufacturer | Sample size (nnn) | Sum of ttt (∑t\sum t∑t) | Sum of t2t^2t2 (∑t2\sum t^2∑t2) | Unbiased estimate of the mean | Unbiased estimate of the variance |
|---|---|---|---|---|---|
| Manufacturer P | 75 | 1860 | 46246.4 | 24.8 | 1.6 |
| Manufacturer Q | 80 | 2040 | 52494 | mmm | vvv |
Calculate the value of mmm and the value of vvv.
The engineer believes that the mean charging time of capacitors from Manufacturer P is shorter than the mean charging time of capacitors from Manufacturer Q.
Stating your hypotheses clearly, carry out a suitable test to assess the engineer's belief. Use a 5% level of significance and state your critical value.
Explain how you have used the Central Limit Theorem in your answer to part (b).
616 exam-style questions on Edexcel A Level Maths The Normal Distribution, covering 3.1 The Normal Distribution, 3.2 Finding Probabilities for Normal Distributions, 3.3 The Inverse Normal Distribution Function, 3.4 The Standard Normal Distribution, 3.5 Finding the mean and standard deviation, 3.6 Approximating a Binomial Distribution, and 3.7 Hypothesis Testing with the Normal Distribution. Each one has a worked solution and a mark scheme showing where the marks go.