At a recent meeting, it was decided to go ahead with the introduction of a new product if “interested consumers would be willing, on average, to pay $20.00 for the product.” A study was conducted, with 315 random interested consumers indicating that they would pay an average of $18.14 for the product. The standard deviation was $2.98.
a. Identify the reference value for testing the mean for all interested consumers.
b. Identify the null and research hypotheses for a two-sided test using both words and mathematical symbols.
c. Perform a two-sided test at the 5% significance level and describe the result.
d. Perform a two-sided test at the 1% significance level and describe the result.
e. State the p-value as either p > 0.05, p < 0.05, p < 0.01, or p < 0.001.