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 new taste. We are interested in determining if more than 21% of the population will like the new soft drink.

A. Set up the null and the alternative hypotheses.

B. Determine the test statistic.  

C. Determine the p-value.

D. Using a=.05, test to determine if more than 21% of the population will like the new soft drink.  

Please show all work and formulas.  

Thank you,

Answer 1

The null hypothesis is: p <= 0.21

The alternative hypothesis is: p > 0.21

Since the confidence interval for this problem is 95%

The critical value for this is 1.960

So the alpha is .05, the p value is equal to 0.05/2 = 0.025
since it is a 2 tailed test. (letter b)

So p value = 0.025 < 0.5, therefore, reject null
hypothesis. More than 21% like the new soft drink.

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