Question

A factory produces bags of rubber bands. A bag of rubber bands has five different sizes: extra large (XL), large (L), medium (M), small (S), and extra small (XS). A quality control specialist collects a random sample of 450 rubber bands from the bagging machine and calculates a chi-square goodness-of-fit test to see if the frequencies for each size in the sample match the hypothesized distribution. The quality control specialist will test his sample against the following null hypothesis.H0:pXL=0.10,pL=0.20,pM=0.40,pS=0.20,pXS=0.10 How many medium rubber bands are expected in the random sample of 450 rubber bands?

Answer 1

180

Just took the test

Answer 2

The expected frequency is 90

Explanation:

If the given probabilities are taken as observed

pXL=0.10, 450*0.1= 45

pL=0.20, 450*0.2= 90

pM=0.40, 450*0.4= 180

pS=0.20, 450*0.2= 90

pXS=0.10 450*0.1= 45

We can assign the expected frequencies to be 450/5= 90 each

The chi square goodness fit test can be calculated as

Observed Expected (o-e) (o-e)² (o-e)² /e

45 90 -45 2025 22.5

90 90 0 0 0

180 90 90 8100 90

90 90 0 0 0

45 90 -45 2025 22.5

∑ 135

χ²= 135

The χ² value at 0.05 is 9.49

The result is significant.