27. Sales of Children's Books The market share for sales of children's books in 2013 was as follows (Source: PublishersWeekly.com).
| Barnes and Noble | Amazon | Others |
|---|---|---|
| 23% | 20% | 57% |
Suppose a survey of 1000 children's book sales this year showed 200 sold by Barnes and Noble, 220 sold by Amazon, and 580 sold by all others. Test whether the population proportions have changed, using level of significance .
11.1.27
: The random variable does not follow the distribution specified in .
Checking the conditions, the expected frequencies are
Because none of these expected frequencies is less than one, and none of the expected frequencies is less than five, the conditions for performing the goodness of ft test are met.
. Reject if .
.
Compare with is . Therefore, we reject . There is evidence that the variable seller does not follow the distribution specified in . In other words, there is evidence that the market share for sales of children's books has changed.