Question

Bentley Foods, 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 14 percent of the population would prefer the pizza over other frozen pizza currently available. To determine preferences, a sample of 1000 consumers was obtained; 172 indicated that they would prefer the new product over existing brands.

a. State the null and alternate hypotheses.  

b. Compute the standard error of the proportion.  

c. Calculate the z statistic. Using a 95% significance level, can you reject the null hypothesis? (Hint: for 95% and a one-tailed test, z = 1.645; or for a two-tailed test, z = 1.96.)

Answer 1

a)

H0: p <= 0.14

Ha: p > 0.14

b)

Standard error = Sqrt( p( 1 - p) / n )

= Sqrt( 0.14 * 0.86 / 1000)

= 0.01097

c)

Sample proportion = 172 / 1000 = 0.172

Test statistics

Z = - p / sqrt( p( 1 - p) / n)

= 0.172 - 0.14 / 0.01097

= 2.916

c)

At 0.05 significance level, critical value is z = 1.645

Since test statistics > 1.645, we have sufficient evidence to reject H0.

We conclude at 0.05 level that we have enough evidence to support the claim that at least 14% of the  

population would prefer the pizza over frozen pizza currently available.