Example 1 The manufacturer of an interior latex paint claims that one coat covers 400 square feet per gallon on interior walls. A painter keeps track of coverage for 6 gallons of paint and finds that the average coverage over the 6 gallons is 383.33 square feet with a standard deviation of 20.66. The painter would like to know if, at an alpha=0.05 level, he has enough evidence to claim that the paint coverage is less than the manufacturer's claim. What are the null and alternative hypotheses? What is the critical value? The test statistic? Do you reject or fail to reject the null? Is this decision sensitive to alpha? Justify your answer. Critical Value Click to add text Alpha Normal Distribution T Distribution One Tailed Two Tailed One Tailed Two Tailed 0.1 1.282 1.645 1.476 2.015 0.05 1.645 1.96 2.015 2.571 0.01 2.326 2.576 3.365 4.032