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

Confidence interval = ( 0.7991, 0.8647 )

Explanation:

Sample size = n = 351

number of successes = X = 292

Sample proportion = P =
`(X)/(n)`

=
`(292)/(351)`

= 0.831908831

confidence interval = 90%

Critical Z value = 1.6449 [by using excel]

Confidence interval = P ± Z
`\sqrt{P((1-P))/(n)}`

Where P = Sample proportion

Z = critical value

n = sample size

Confidence interval = 0.831908831 ± 1.6449
`\sqrt{0.831908831((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 )