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2.5 Statistical Hypothesis Testing

2.5 Statistical Hypothesis Testing

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Question 230

A materials engineer is monitoring the cooling of a specialized ceramic component. The temperature of the component, TTT ∘C^\circ\text{C}∘C, is recorded at various times, ttt minutes, after it is removed from a kiln, where 4≤t≤364 \le t \le 364≤t≤36.

The engineer calculated the regression line of TTT on ttt and found it to be

T=165.4−2.85t T = 165.4 - 2.85t T=165.4−2.85t
a.

Give an interpretation of the gradient of the regression line.

[1]
b.

Use the regression line to estimate the temperature of the component 45 minutes after it was removed from the kiln.

[1]
c.

Comment on the reliability of your estimate in part (b), giving a reason for your answer.

[2]
d.

Using the regression line of TTT on ttt and the following summary statistics:

∑T=1300.8∑T2=149 856.72∑t2=5850n=12 \sum T = 1300.8 \quad \sum T^2 = 149\,856.72 \quad \sum t^2 = 5850 \quad n = 12 ∑T=1300.8∑T2=149856.72∑t2=5850n=12

Show that the product moment correlation coefficient (PMCC) for these data is −0.982-0.982−0.982 to 3 decimal places.

[4]
e.

A scatter diagram of the engineer's data shows the points distributed tightly around a straight line with a negative gradient.

With reference to both the scatter diagram and the correlation coefficient, discuss the suitability of a linear regression model to describe the relationship between ttt and TTT.

[2]
Markscheme

2.5 Statistical Hypothesis Testing Questions

  1. A Level
  2. /Maths
  3. /2.5 Statistical Hypothesis Testing

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.

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