Question

B. Do Americans like their pizza to be spicy or not spicy? Currently, a restaurant which specializes in pizza only makes non-spicy pizza. It is now considering offering spicy pizza to its customers but, only if it can be convinced that more than 30% of its pizza eating customers would prefer spicy pizza. Over a one-week period, it prepared non-spicy pizza and a limited amount of spicy pizza in order to conduct an experiment. During this period of its offer, it randomly selected 60 of its pizza ordering customers and gave them pieces of both spicy and non-spicy pizza at no cost. Twenty-seven of these randomly selected customers stated that they preferred the spicy pizza. At the .01 level of significance, should the restaurant start offering spicy pizza to its customers?

state the two hypotheses calculate the value of the test statistic, z calculate the p-value of this test determine the critical value of z compare the value of z with the critical value of z and compare the p-value with α and state whether or not the null hypothesis should be rejected and write a concluding statement

Answer 1

Here null and alternate hypothesis are

Now and q=1-n=1-0.30=0.70

First we will find test statistic

Now P-value for P(z>2.54)=0.0055

The z-critical value for a right-tailed test, for a significance level of alpha = 0.01 is

z_c​=2.33

As the P-value(0.0055) is  less than alpha(0.01) we reject the null hypothesis

As z critical value (2.33) is less than test statistic 2.54 we reject the null hypothesis.

As we reject the null hypothesis we can conclude that  more than 30% of its customes prefer spicy pizza.