Question

6. A food company is planning to market a new type of frozen yogurt. The company’s management will market the yogurt only if at least 45% of the people like it. The company’s research department selected a random sample of 400 persons and asked them to taste this yogurt. Of these 400 persons, 112 said they liked it. Testing at the 2.5% significance level, can the management conclude that they should market the yogurt? Use a p-value test.

Answer 1

6)

Solution :

This is the left tailed test .

The null and alternative hypothesis is

H₀ : p = 0.45

H_a : p < 0.45

= x / n = 112 / 400 = 0.28

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.28 - 0.45/ [(0.45 * 0.55) / 400]

= -6.834

P-value = 0.000

= 0.05

P-value <

We can not conclude that they should market the yogurt only if at least 45% of the people like it.