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2.5 Statistical Hypothesis Testing

2.5 Statistical Hypothesis Testing

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Question 204

An environmental scientist is investigating the effect of daily light intensity, LLL lux, on the vertical growth rate of a specific type of algae, GGG mm/day, in a controlled lab environment. Over a period of 12 days, the following summary statistics were recorded:

∑L=600,∑L2=32800,∑G=156,SGG=450 \sum L = 600, \quad \sum L^2 = 32800, \quad \sum G = 156, \quad S_{GG} = 450 ∑L=600,∑L2=32800,∑G=156,SGG​=450
a.

Calculate the value of SLLS_{LL}SLL​.

[1]
b.

The scientist calculated the product moment correlation coefficient between LLL and GGG to be 0.925, correct to 3 decimal places.

State, giving a reason, whether or not this correlation coefficient supports the use of a linear regression model to describe the relationship.

[1]
c.

State, giving a reason, why light intensity would be the explanatory variable.

[1]
d.

Find the value of SLGS_{LG}SLG​.

[2]
e.

Calculate a suitable linear regression equation to model the relationship between growth rate and light intensity.

[4]
f.

Calculate the standard deviation of LLL.

[1]
g.

The scientist uses this model to estimate the growth rate on a day where the light intensity is 95 lux.

State the value of the scientist’s estimate for GGG.

[1]
h.

Given that the values of LLL in the sample are all within 2.5 standard deviations of the mean,

comment, giving your reason, on the reliability of this estimate.

[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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