Question

Last year, a soft drink manufacturer had 21% of the market. In order to increase their portion of the market, the manufacturer has introduced a new flavor in their soft drinks. A sample of 400 individuals participated in the taste test and 100 indicated that they like the taste. We are interested in determining if more than 21% of the population will like the new soft drink at the significance level 0.05.

The p-value is best interpreted as the following:

a. The p-value indicates the probability of observing the proportion of people who like new flavor equal to 25% or lower in the sample of 400 individuals, if actual proportion of people who like the new flavor is 21%.

b. The p-value indicates the probability of observing the proportion of people who like new flavor equal to 25% or greater in the sample of 400 individuals, if actual proportion of people who like the new flavor is 21%.

c. The p-value indicates the probability of observing the proportion of people who like new flavor equal to 21% or greater in the sample of 400 individuals, if actual proportion of people who like the new flavor is 21%.

Answer 1

Explanation:

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

a) For the null hypothesis,

P = 0.21

For the alternative hypothesis,

P > 0.21

Considering the population proportion, probability of success, p = 0.21

q = probability of failure = 1 - p

q = 1 - 0.21 = 0.79

Considering the sample,

Sample proportion, p = x/n

Where

x = number of success = 100

n = number of samples = 400

p = 100/400 = 0.25 = 25%

The z statistic is calculated and the probability value is determined

The P-value describes the strength of the evidence against the null hypothesis. Therefore, the p-value is best interpreted as the following:

b. The p-value indicates the probability of observing the proportion of people who like new flavor equal to 25% or greater in the sample of 400 individuals, if actual proportion of people who like the new flavor is 21%.