In: Statistics and Probability
Exhibit: Soft Drinks.
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.
Round your solutions for this Exhibit to 4 decimal places.
1. Refer to the Exhibit Soft Drinks.
Compute the test statistic.
Solution:
Point estimate = sample proportion = = x / n = 0.25
This a right (One) tailed test.
The null and alternative hypothesis is,
Ho: p = 0.21
Ha: p 0.21
Test statistics
z = ( - ) / *(1-) / n
= ( 0.25 - 0.21) / (0.21*0.79) / 400
= 1.964
P-value = P(Z > z )
= 1 - P(Z < 1.964 )
= 1 - 0.9752
= 0.0248
The p-value is p = 0.0248, and since p = 0.0248 < 0.05, it is concluded that the null hypothesis is rejected.