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Quiz # 4 STA2023
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confidence intervals, hypothesis tests for proportions
Provide all of your answers/explanations/work in the spaces provided. However, you may attach
additional work if you want to. Write your quiz up with your name, date, and the time and days that you
attend the class. Show all work for full credit. Your submitted quiz should be neat, clear and detailed. It
should not be a rough draft. When in doubt, include as much relevant, correct information pertaining to
your answer as possible. Remember, start early and seek out help if you “get stuck.” There are three
printed pages to this quiz.
1. (11 pts. total) An association of Christmas tree growers in Indiana sponsored a sample survey of
Indiana households to help improve the marketing of Christmas trees. The researchers decided to
use a random telephone survey and estimated that each telephone interview would
take about 2 minutes. Nine trained students in agribusiness marketing were to
make the phone calls between 1:00 pm and 8:00 pm on a Sunday. After
discussing problems related to people not being at home or being unwilling to
answer the questions, the survey team proposed a sample size of 500. Several
of the questions asked demographic information about the household; the key
questions of interest had responses of “Yes” or “No.” For example, “Did you have
a Christmas tree this year?” Of the 500 respondents, 421 answered “Yes” to this particular
question.
a. Construct, showing all values substituted into your formula, a 95% confidence interval
for the proportion of all Indiana households who had a Christmas tree last year. The
confidence interval should be given in interval notation.
b. Interpret the confidence interval given in part a. Remember to interpret the result in full
english sentences (no notation, use story problem situation with units of measure where
applicable).
c. State in detail, citing values from the story problem situation, all of the reasons why we
are allowed to construct the confidence interval from part a.
