Question

Last year, a soft drink manufacturer had 20% 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 96 indicated that they like the taste.

Suppose that the manufacturer is interested in determining if more than 20% of the population will like the new soft drink. State the null and alternative hypotheses.  

Find the standard error of the proportion

Find the critical value associated with a 2.5% significance level for this test.

se the critical value approach and determine whether the null hypothesis stated in ‘a’ above should be rejected or not at the 2.5% significance level.

Answer 1

The following information is provided: The sample size is N = 400 , the number of favorable cases is X = 96, and the sample proportion is , and the significance level is α=0.025

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

less than or equal to 20% likes the taste of the new flavor of the soft drink

more than 20% likes the taste of the new flavor of the soft drink

This corresponds to a right-tailed test, for which a z-test for one population proportion needs to be used.

(2) Rejection Region

Based on the information provided, the significance level is α=0.025, and the critical value for a right-tailed test is z_c = 1.96

(3) Test Statistics

The z-statistic is computed as follows:

(4) Decision about the null hypothesis

Since it is observed that z = 2 >zc​=1.96, it is then concluded that the null hypothesis is rejected.

Using the P-value approach: The p-value is p = 0.0228 , and since p = 0.0228 <0.025, it is concluded that the null hypothesis is rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population proportion p is greater than p0​, at the α=0.025 significance level.

Hence, more than 20% likes the taste of the new flavor of the soft drink