Bentley Foods, Inc., a large manufacturer of frozen foods, has developed a new line of frozen pizza. Management has agreed to begin producing and marketing the new line if at least 15% of the population would prefer the pizza over other frozen pizzas currently available. To determine preferences, a sample of 1,000 consumers was obtained; 172 indicated that they would prefer the new product over existing brands.
a. State the null and alternative hypothesis.
Ho : p £ .15
Ha : p > .15
b. Compute the standard error of the proportion.
c. Calculate the z-statistic. What is the probability of obtaining this value of the z-statistic if the null hypothesis is true?
d. The research manager for Bentley Foods is comfortable using the .05 significance level. Should the null hypothesis be rejected?
e. At this significance level, what is the critical sample proportion?