Business Statistics

Chapter 10 | Statistical Inference: Hypothesis Testing for Single Populations 337

Step 5: Collect the sample data

A random sample of 130 purchasers indicates that 50 customers have purchased

20colour television. Hence,

p

= Sample proportion

50

0.3846

130

= =

p = Population proportion = 0.30

q = 1 – p = 1 – 0.30 = 0.70

Step 6: Analyse the data

The z statistic for a population proportion with np  5 and nq  5 can be com-

puted as

0.3846 0.30

2.1052

(0.30) (0.70)

130

p p

z

pq

n

− −

= = =

×

Step 7: Arrive at a statistical conclusion and business implication

The observed value of z falls in the rejection region (2.1052 > 1.96). So, the null

hypothesis is rejected ...