Question

4) In a certain state a politician claims that 20% of residents are on food stamps. Suppose 550 residents are surveyed and 100 are on food stamps. At the α = 0.05 level of significance, test the claim of the politician.

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H0 : p = 0.20

Ha : p 0.20

= x / n = 100/550 = 0.1818

P0 = 0.20

1 - P0 = 1 -0.20 =.0.80

Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

=0.1818 -0.20/ [0.20*(0.80) /550 ]

= -1.067

P(z < -1.067) = 0.1430 *2 = 0.2860

P-value = 0.2860

= 0.05

0.2860 >  0.05

Fail to reject the null hypothesis .

There is insufficient evidence to suggest that the α = 0.05 level of significance, test the claim of the politician.