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. Group of answer choices.534.1660.824.5
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. Group of answer choices.534.1660.824.5
Solution
To answer this question, we will perform a one-sample proportion hypothesis test. Here are the steps:
Step 1: State the hypotheses. The first step is to state the null hypothesis and the alternative hypothesis.
Null hypothesis: p = 0.22 (22% of the population will like the new soft drink) Alternative hypothesis: p > 0.22 (more than 22% of the population will like the new soft drink)
Step 2: Formulate an analysis plan. For this analysis, the significance level is defined as 0.05. The sample proportion (p̂) is 80/400 = 0.20.
Step 3: Analyze sample data. Using the sample data and assuming the null hypothesis is true, calculate the value of the test statistic. The test statistic is a z-score (z).
z = (p̂ - p) / sqrt[(p(1 - p) / n] z = (0.20 - 0.22) / sqrt[(0.22(1 - 0.22) / 400] z = -0.02 / sqrt[0.1716 / 400] z = -0.02 / 0.0207 z = -0.966
Step 4: Interpret the results. If the test statistic is greater than the critical value, this suggests that we should reject the null hypothesis.
We find the critical value of z in a z-table to be 1.645 for a one-tailed test at a 5% significance level. Since -0.966 is not greater than 1.645, we do not reject the null hypothesis.
Therefore, we do not have enough evidence at the 5% significance level to support the claim that at least 22% of the population will like the new soft drink.
Similar Questions
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 choicesdo not reject H0revise horeject Ho
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.What is the test statistic? Group of answer choices-.97-.74.79.47
A marketing survey is conducted in which students are to taste two different brands of soft drink.Their task is to correctly identify the brand tasted.A random sample of 200 students is taken.Assume that the students have no ability to distinguish between the two brands. b.The probability is 90%that the sample percentage is contained within what symmetrical limits of the population percentage?Identify the limits of the population percentage. The lower limit is The upper limit is (Round to four decimal places as needed.)
Analyse two ways in which a soft drinks manufacturer might segment the market for its products
A company wants to investigate the initial reactions of heavy soft-drink usersto a new “all natural” soft drink.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.