A new soft drink is being market tested. A sample of 400 individuals participated in the taste test and 80 indicated they like the taste. At a 5% significance level, test to determine if at least 22% of the population will like the new soft drink. conclusion for null hypothesis isGroup of answer choicesreject Hodo not reject H0revise ho
Question
A new soft drink is being market tested. A sample of 400 individuals participated in the taste test and 80 indicated they like the taste. At a 5% significance level, test to determine if at least 22% of the population will like the new soft drink. conclusion for null hypothesis isGroup of answer choicesreject Hodo not reject H0revise ho
Solution
To answer this question, we need to conduct a hypothesis test for a proportion. Here are the steps:
Step 1: State the null hypothesis (H0) and the alternative hypothesis (H1). The null hypothesis (H0): p = 0.22 (22% of the population will like the new soft drink) The alternative hypothesis (H1): p > 0.22 (More than 22% of the population will like the new soft drink)
Step 2: Choose the significance level. The significance level is given as 5% or 0.05.
Step 3: Calculate the test statistic. The test statistic for a proportion is a z-score (z). The formula for the z-score is (p̂ - p) / sqrt [ p(1 - p) / n ] where p̂ is the sample proportion, p is the population proportion, and n is the sample size. In this case, p̂ = 80/400 = 0.20, p = 0.22, and n = 400. So, z = (0.20 - 0.22) / sqrt [ 0.22(1 - 0.22) / 400 ] = -1.65
Step 4: Determine the critical value. The critical value for a one-tailed test at the 5% significance level is 1.645.
Step 5: Make a decision to reject or not reject the null hypothesis. Since the calculated z-score (-1.65) is less than the critical value (1.645), we do not reject the null hypothesis.
Conclusion: At a 5% significance level, there is not enough evidence to conclude that more than 22% of the population will like the new soft drink. So, we do not reject H0.
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