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Sauron [17]
3 years ago
5

A survey of 1000 air travelers1 found that 60 % prefer a window seat. The sample size is large enough to use the normal distribu

tion, and a bootstrap distribution shows that the standard error is StartItalic UpperWord S E EndItalic equals 0.015.
Use a normal distribution to find a 90 % confidence interval for the proportion of air travelers who prefer a window seat.


Round your answers to three decimal places.


The 90% confidence interval is _____________to ____________
Mathematics
1 answer:
stira [4]3 years ago
3 0

Answer:

The 90% confidence interval is 0.575 to 0.625.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence interval 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

Z is the zscore that has a pvalue of 1 - \frac{\alpha}{2}.

For this problem, we have that:

n = 1000, \pi = 0.60

90% confidence interval

So \alpha = 0.1, z is the value of Z that has a pvalue of 1 - \frac{0.1}{2} = 0.95, so z = 1.645.

The lower limit of this interval is:

\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.60 - 1.645\sqrt{\frac{0.60*0.40}{1000}} = 0.575

The upper limit of this interval is:

\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.60 + 1.645\sqrt{\frac{0.60*0.40}{1000}} {119}} = 0.625

The 90% confidence interval is 0.575 to 0.625.

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