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2.5 Statistical Hypothesis Testing

2.5 Statistical Hypothesis Testing

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Question 256

An industrial chemist is studying the relationship between the UV intensity index, uuu, and the yield of a refined polymer, yyy grams. The chemist records the results for 12 different batches. The summary statistics are as follows:

∑u=84,∑y=156,∑u2=628,∑y2=2118 \sum u = 84, \quad \sum y = 156, \quad \sum u^2 = 628, \quad \sum y^2 = 2118 ∑u=84,∑y=156,∑u2=628,∑y2=2118 ∑uy=1146,Suu=40,Syy=90 \sum uy = 1146, \quad S_{uu} = 40, \quad S_{yy} = 90 ∑uy=1146,Suu​=40,Syy​=90
a.

Find the mean and variance of the recorded yields.

[2]
b.

The chemist believes that increased UV intensity results in a higher polymer yield.

(i) Calculate the product moment correlation coefficient (PMCC) between uuu and yyy. (ii) State, with a reason, whether or not this value supports the chemist's belief.

[3]
c.

Find the least squares regression line of yyy on uuu in the form y=a+buy = a + buy=a+bu. Give the values of aaa and bbb to 3 significant figures.

[3]
d.

Estimate the yield when the UV intensity index is 9.2.

[1]
e.

The coding z=5y−50z = 5y - 50z=5y−50 is used to transform the yield data.

Find an equation of the least squares regression line of zzz on uuu in the form z=c+duz = c + duz=c+du.

[2]
f.

Find: (i) the variance of the transformed yields zzz. (ii) the product moment correlation coefficient between zzz and uuu.

[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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