Skip to content

Course home

2.5 Statistical Hypothesis Testing

2.5 Statistical Hypothesis Testing

EasyMediumHard
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250251252253254255256257258259260261262263264265266267268269270271272273
Question 222

A chemical engineer is studying the effect of a specific catalyst concentration, CCC (mol/L), on the rate of gas production, RRR (mL/s). The data for 8 experimental trials are recorded in the table below:

Trial12345678Concentration (C)0.050.120.180.250.320.440.580.75Rate (R)1.42.94.23.86.55.99.18.2\begin{array}{|l|c|c|c|c|c|c|c|c|} \hline \text{Trial} & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ \hline \text{Concentration } (C) & 0.05 & 0.12 & 0.18 & 0.25 & 0.32 & 0.44 & 0.58 & 0.75 \\ \hline \text{Rate } (R) & 1.4 & 2.9 & 4.2 & 3.8 & 6.5 & 5.9 & 9.1 & 8.2 \\ \hline \end{array}TrialConcentration (C)Rate (R)​10.051.4​20.122.9​30.184.2​40.253.8​50.326.5​60.445.9​70.589.1​80.758.2​​

a.

Calculate Spearman’s rank correlation coefficient between catalyst concentration and production rate, giving your answer to 3 decimal places.

[4]
b.

Test, at the 5% significance level, whether there is evidence of a positive correlation between catalyst concentration and production rate. State your hypotheses clearly.

[3]
c.

A junior researcher suggests that the product moment correlation coefficient (PMCC) should be used instead. The PMCC for this specific data set is calculated to be 0.924 (to 3 decimal places).

Use this PMCC value to test for evidence of a positive linear correlation at the 5% significance level.

[2]
d.

Comparing your results from parts (b) and (c), explain what the relative values of these coefficients suggest about the relationship between catalyst concentration and gas production rate.

[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.

Question bank