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Chapter 8: Problem 27

A taste test is done to see whether a person can tell Coke from Pepsi. In each case, 20 random and independent trials are done (half with Pepsi and half with Coke) in which the person determines whether she or he is drinking Coke or Pepsi. One person gets 13 right out of 20 trials. Which of the following is the correct figure to test the hypothesis that the person can tell the difference? Explain your choice.

Short Answer

Expert verified
One would calculate the Z statistic using the binomial test formula: \(Z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}\). After calculating the Z score, one would look up the critical value in a Z-table or with software to decide whether to accept or reject the null hypothesis.

Step by step solution

01

Understand the problem and set up the hypotheses

The first step is all about understanding the problem and setting the hypotheses. The null hypothesis \(H_0\) is that the person is guessing: the probability of guessing correctly, \(p_0\), is 0.5. The alternative hypothesis \(H_a\) is that the probability of guessing correctly, \(p\), is different from 0.5.
02

Calculate the test statistic

In this case, one person got 13 out of 20 trials right, so the sample proportion \(\hat{p}\) is 13/20 = 0.65. The test statistic \(Z\) is calculated using the formula \(Z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}\), where \(\hat{p}\) is the sample proportion, \(p_0\) is the population proportion under the null hypothesis, and \(n\) is the sample size. In this case, \(Z = \frac{0.65 - 0.5}{\sqrt{\frac{0.5(1-0.5)}{20}}}\) can be calculated.
03

Determine Critical Value and Make Decision

Refer to the standard normal (Z) table or use statistical software to find the critical value for the Z statistic. If the absolute value of the test statistic is less than the critical value, then do not reject the null hypothesis. If the absolute value of the test statistic is greater than the critical value, then reject the null hypothesis.

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Most popular questions from this chapter

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