Question

The mayor of a large city claims that 30 % of the families in the city earn more than $ 100,000 per year; 60 % earn between $ 30,000 and $ 100,000 (inclusive); 10 % earn less than $ 30,000 per year.

In order to test the mayor’s claim, 285 families from the city are surveyed and it is found that:

100 of the families earn more than $ 100,000 per year;
150 of the families earn between $ 30,000 and $ 100,000 per year (inclusive);
35 of the families earn less $ 30,000.

Test the mayor’s claim based on 5 % significance level.

Answer 1

Null hypothesis : H₀ : The distribution is same as mayor claims.

Alternative hypothesis : H₁ : The distribution is different than what mayor claims

The expected value for number of families who earn more than $100,000 per year would be ,

The expected value for number of families who earn between$30,000 and $100,000 per year would be ,

The expected value for number of families who earn less than $30,000 per year would be ,

Earnings	Observed Value(O)	Expected Value(E)
more than $100,000	100	85.5
between $30,000 and $100,000	150	171
less than $30,000	35	28.5

The test statistic would be given by,

The degree of freedom would be given by,

df = n - 1 = 3 - 1 = 2

The critical value corresponding to 5% significance level and 2 degrees of freedom is 5.99

Since the test statistic is greater than critical value, we will reject the null hypothesis. Hence the mayor's claim is not supported.