Question

In: Statistics and Probability

Exhibit: Soft Drinks. Last year, a soft drink manufacturer had 21% of the market. In order...

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.

Solutions

Expert Solution

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.


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