Question

Using a significance level of 0.01, test the claim that the proportion of toothpaste brands with ADA seal is less than 0.60. Assume in a sample of 100, 48 have the ADA seal

Answer 1

Solution :

This is the left tailed test .

The null and alternative hypothesis is

H₀ : p = 0.60

H_a : p < 0.60

= x / n = 48 / 100 = 0.48

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.48 - 0.60 / [(0.60 * 0.40) / 100]

= -2.45

P(z < -2.45) = 0.0071

P-value = 0.0071

= 0.01

P-value <

Reject the null hypothesis .

There is sufficient evidence to suggest that  the proportion of toothpaste brands with ADA seal is less than 0.60 .