Chapter 10.3, Problem 10.29ACB

Package design influences taste. Can the package design of a food product, along with accompanying sounds, influence how the consumer wilt rate the taste of the product? A team of experimental psychologists reported on a study that examined how rounded or angular package shapes and high- or low-pitched sounds can convey information about the taste (sweetness and sourness) of a product (Food Quality and Preference, June 2014). Study participants were presented with one of two types of packaging displayed on a computer screen monitor: rounded shape with a low-pitched sound or angular shape with a high-pitched sound Assume that half of the participants viewed the rounded packaging and half viewed the angular packaging. After viewing the product, each participant rated whether the packaging was more appropriate for either a sweet- or a sour-tasting food product. A summary of the results (numbers of participants) for a sample of 80 participants is shown in the following contingency table. (These data are simulated based on the results reported in the article).

1. a. Specify the null and alternative hypotheses for testing whether the package design and sound pitch combination influences the consumer’s opinion on the product taste.
2. b. Assuming the null hypothesis is true, find the expected number in each cell of the table.
3. c. Use the expected numbers and observed counts in the table to compute the chi-square test statistic.
4. d. The observed significance level (p-value) of the test is approximately 0. (You can verify this result using statistical software.) For any reasonably chosen value of α, give the appropriate conclusion.