Question

Gary is studying the prevalence of regional dialects. He surveyed 351 people in a region and asked what words they used for certain things. Gary found that 292 of the respondents referred to soft drinks as "pop," as opposed to "soda" or "cola." Create a 90% confidence interval for the proportion of people in this region who refer to soft drinks as "pop." Use Excel to create the confidence interval, rounding to four decimal places.

Answer 1

Answer:

Confidence interval = ( 0.7991, 0.8647 )

Step-by-step explanation:

Sample size = n = 351

number of successes = X = 292

Sample proportion = P = $\frac{X}{n}$

                                     =  $\frac{292}{351}$

                                     = 0.831908831

confidence interval = 90%

Critical Z value  = 1.6449   [by using excel]

Confidence interval = P ± Z $\sqrt{P\frac{(1-P)}{n}}$

Where P = Sample proportion

           Z = critical value

           n = sample size

Confidence interval =  0.831908831 ± 1.6449 $\sqrt{0.831908831\frac{(1-0.831908831)}{351}}$

                                = 0.831908831 ± 1.6449 × 0.0200

                                = 0.831908831 ± 0.032898

 Lower limit             = 0.831908831 - 0.032898 = 0.7991

Upper limit               = 0.831908831 + 0.032898 = 0.8647

Confidence interval = ( 0.7991, 0.8647 )