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23.04.2020 •
Mathematics
A survey of 542 consumers reveals that 301 favor the new design for a product. Construct a 90% confidence interval for the true proportion of all consumers who favor the design.
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Ответ:
The 90% confidence interval for the true proportion of all consumers who favor the design is (0.52, 0.59).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of , we have the following confidence interval of proportions.
In which
z is the zscore that has a pvalue of .
For this problem, we have that:
90% confidence level
So , z is the value of Z that has a pvalue of , so .
The lower limit of this interval is:
The upper limit of this interval is:
The 90% confidence interval for the true proportion of all consumers who favor the design is (0.52, 0.59).
Ответ: