A leading toothpaste manufacturer advertises that, in a recent medical study, 70% of the people tested had brighter teeth after using its toothpaste (called Very Bright) as compared to using the leading competitor’s brand (called Brand X). The advertisement continues, “Therefore, use Very Bright and get brighter teeth.” In point of fact, the data upon which these statements were based were collected from a random sample of 10 employees from the manufacturer’s Pasadena plant. In the experiment, each employee used both toothpastes. Half of the employees used Brand X for 3 weeks, followed by Very Bright for the same time period. The other half used Very Bright fi rst, followed by Brand X. A brightness test was given at the end of each 3-week period. Thus, there were two scores for each employee, one from the brightness test following the use of Brand X and one following the use of Very Bright. The following table shows the scores (the higher, the brighter):
a. What is the alternative hypothesis? Use a directional hypothesis.
b. What is the null hypothesis?
c. Using ?? = 0.051 tail, what do you conclude?
d. What error might you be making by your conclusion in partc?
e. To what population does your conclusion apply?
f. Does the advertising seem misleading?