Question

according to a global nielson report, 66% of north americans pay more attention to the nutritional information on a package than they did two years ago. a random sample of 400 individuals from north america showed that 300 people stated that they did pay more attention to the nutritional information on a package than they did two years ago. we are interested in testing to see if the proportion has changed. calculate the p-value and assess the strength of evidence against the null hypothesis.

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H₀ : p = 0.66

H_a : p > 0.66

= x / n = 300 / 400 = 0.75

P₀ = 0.66

1 - P₀ = 0.34

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.750 - 0.66 / [(0.66 * 0.34) / 400]

= 3.8

P(z > 3.8) = 1 - P(z < 3.8) = 0.0001

P-value = 0.0001