Question

Using a significance level of 0.05, test the claim that the proportion of preschool children with protein deficient diets is less than 70% if in a sample of 300, 180 were deficient

Answer 1

Solution :

This is the left tailed test .

The null and alternative hypothesis is

H0 : p = 0.70

Ha : p < 0.70

n =300

x = 180

= x / n = 180 / 300 = 0.60

P0 = 0.70

1 - P0 = 1 - 0.70 = 0.30

Test statistic = z

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

=0.60 - 0.70 / [(0.70*0.30) / 300]

= -3.78

Test statistic = z = -3.78

P(z < -3.78 ) = 0.0001

P-value = 0.0001

= 0.05

P-value <

0.0001 < 0.05

Reject the null hypothesis .

There is sufficient evidence to suggest that