BN001, BN009 Mathematics 4

Hypothesis Testing

Worksheet 3

Question 1

A company is manufacturing components with 3 separate production

processes. During the production process, 4 important faults in the

components are identified and the management seek to identify whether there

is a link between production method and identified fault. The company

recorded each incidence of a component with one fault produced in a given

time-period, sorted by production method and fault. The counts are given in

the table shown

Method 1 Method 2 Method 3

Fault A 126 154 175

Fault B 152 151 142

Fault C 169 157 145

Fault D 178 153 125

Determine, using an appropriate statistical test, whether or not the 4 faults are

arising equally across the three production methods.

Question 2

As part of a study into the effects of smoking, a group of 70 students counted

the number of incidents of respiratory related illness during each of the four

seasons, among non-smokers (NS), light smokers (LS) and heavy smokers

(HS). The results are shown in the following table.

NS LS HS

Winter 8 14 16

Spring 4 11 10

Summer 0 4 6

Autumn 1 6 6

Determine, using an appropriate statistical test, whether there is a link

between smoking and respiratory health across the four seasons.

Test for independence

The steps involved are:

1. Frame the null and alternative hypothesis.

2. Decide the level of significance, e.g. 0.05 or 0.1.

3. Look up critical values.

4. Calculate the value of 2, from the data.

5. The null hypothesis is rejected if this exceeds the critical value.