Question

8.29 In a survey of 1,003 adults concerning complaints about restaurants, 732 complained about dirty or ill-equipped bathrooms and 381 complained about loud or distracting diners at other tables.

a. Construct a 95% confidence interval estimate for the population proportion of adults who complained about dirty or ill-equipped bathrooms )

b. Construct a 95% confidence interval estimate for the population proportion of adults who complained about loud or distracting diners at other tables.

c. How would the manager of a chain of restaurants use the results of (a) and (b)?

Answer 1

Given that, in a survey of 1,003 adults concerning complaints about restaurants, 732 complained about dirty or ill-equipped bathrooms and 381 complained about loud or distracting diners at other tables.

A 95% confidence level has significance level of 0.05 and critical value is,

a) n = 1003 and x = 732

sample proportion = 732/1003 = 0.7298

The 95% confidence interval for population proportion is,

The 95% confidence interval is (0.7023, 0.7573)

b) n = 1003 and x = 381

sample proportion = 381/1003 = 0.3799

The 95% confidence interval for population proportion is,

The 95% confidence interval is (0.3499, 0.4099)

c) From part a) we can says that,

The manager can be 95% confident that the population proportion of all adults who complained about dirty or ill equipped bathrooms lies within the interval in a).

From part b) we can says that,

The manager can be 95% confident that the population proportion o all adults who complained about loud or distracting diners at other tables es within the interval in b).