Respuesta :
Answer:
The decision is made using the hypothesis test.
Step-by-step explanation:
The yogurt producer is collecting samples for the number of people who like the new type of yogurt and the number that do not likes the new type.
To arrive a conclusion the yogurt producer must use a hypothesis test for single proportion to determine whether he should market the new product or not.
The hypothesis must be designed as follows:
H₀: The proportion of people who like the new yogurt is less than 50%, i.e. p < 0.50
Hₐ: The proportion of people who like the new yogurt is more than or equal to 50%, i.e. p ≥ 0.50
The significance level of the test is decided to be α.
The test statistic is:
[tex]z=\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]
⇒ The normal distribution is used to approximate the sampling distribution of sample proportion because the sample selected is large, as the yogurt producer is conducting the taste test throughout out the country.
Decision rule: If the p-value of the test is less than α then the null hypothesis is rejected. And vice-versa.
Hence the decision is made using the hypothesis test.
