Skip to content

Course home

2.5 Statistical Hypothesis Testing

2.5 Statistical Hypothesis Testing

EasyMediumHard
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250251252253254255256257258259260261262263264265266267268269270271272273
Question 109

A meteorologist is investigating the relationship between relative humidity, hhh as a percentage, and horizontal visibility, vvv in kilometres (km), at an airport. A random sample of 12 days is selected from the previous year.

The collected data are summarised as follows:

n=12,∑h=816,∑v=156,∑v2=2240,Shh=960,Shv=−384 n = 12, \quad \sum h = 816, \quad \sum v = 156, \quad \sum v^2 = 2240, \quad S_{hh} = 960, \quad S_{hv} = -384 n=12,∑h=816,∑v=156,∑v2=2240,Shh​=960,Shv​=−384
a.

Calculate the product moment correlation coefficient between hhh and vvv.

[3]
b.

Give an interpretation of your product moment correlation coefficient in the context of the study.

[1]
c.

Find the equation of the least squares regression line of vvv on hhh in the form v=a+bhv = a + bhv=a+bh.

[4]
d.

Give an interpretation of the value of bbb in your regression line.

[1]
e.

(i) Use the regression line from part (c) to estimate the visibility for a day with relative humidity of 90%90\%90%.

(ii) Comment on the reliability of your answer in part (i) given that the range of relative humidities in the sample was 52%52\%52% to 84%84\%84%.

[2]
f.

Using the regression line from part (c), the meteorologist estimates that for a humidity decrease of x%x\%x%, there will be an increase of 888 km in horizontal visibility.

Find the value of xxx.

[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