Question

In a survey of 3,778 adults concerning complaints about​ restaurants, 1,436 complained about dirty or​ ill-equipped bathrooms and 1,213 complained about loud or distracting diners at other tables. Complete parts ​(a) through​ (c) below.

a. Construct a 90​% confidence interval estimate of the population proportion of adults who complained about dirty or​ ill-equipped bathrooms.

b. Construct a 90% confidence interval estimate of the population proportion of adults who complaied about loud or distracting diners at other tables.

(round to 4 decimal placed)

Answer 1

The confidence interval for population proportion,"p" for any characteristic is given by :

where is the sample proportion ; and

E is the margin of error and

where is the upper point of the standard normal distribution.

a) Dirty or ill-equipped bathrooms

Here we have :

Thus, the required confidence interval is given by:

0.380095 - 0.012990 < p < 0.380095 + 0.012990

0.367105 < p < 0.393085

0.3671 < p < 0.3931 (Rounded to 4 decimal places)

b) Loud or distracting diners at other tables

Here we have:

Thus, the required confidence interval is given by:

0.321069 - 0.012494 < p < 0.321069 + 0.012494

0.308575 < p < 0.333564

0.3086 < p < 0.3336 (Rounded to 4 decimal places)

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