According to Information Resources Inc., based on sales of teeth-cleaning products, Crest toothpaste controlled a 31.2% share of the market. A researcher from a rival company believes that this figure is high, and that in fact, Crest controls less than 31.2% of the market. A simple random sample of 400 consumers yields 116 use Crest. Does the sample data provide evidence to conclude that the researcher from the rival company is correct (with a = .05)? Use the hypothesis testing procedure outlined below.
a. Formulate the null and alternative hypotheses.
b. State the level of significance.
c. Find the critical value (or values), and clearly show the rejection and nonrejection regions.
d. Compute the test statistic.
e. Decide whether you can reject Ho and accept Ha or not.
f. Explain and interpret your conclusion in part e. What does this mean?
g. Determine the observed p-value for the hypothesis test and interpret this value. What does this mean?
h. Does the sample data provide evidence to conclude that Crest's market share is below 31.2% (with a = .05)?