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kotegsom [21]
3 years ago
7

5. A study found that the average time it took a person to find their dream home was 5.9 months. If a sample of

Mathematics
1 answer:
solong [7]3 years ago
4 0

Answer:

The 95% confidence interval of the mean time it took a person to find their dream home is between 5.64 months and 6.16 months.

Step-by-step explanation:

We have that to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\alpha = \frac{1-0.95}{2} = 0.025

Now, we have to find z in the Ztable as such z has a pvalue of 1-\alpha.

So it is z with a pvalue of 1-0.025 = 0.975, so z = 1.96

Now, find the margin of error M as such

M = z*\frac{\sigma}{\sqrt{n}}

In which \sigma is the standard deviation of the population and n is the size of the sample.

M = 1.96\frac{0.8}{\sqrt{36}} = 0.26

The lower end of the interval is the sample mean subtracted by M. So it is 5.9 - 0.26 = 5.64 months

The upper end of the interval is the sample mean added to M. So it is 5.9 + 0.26 = 6.16 months.

The 95% confidence interval of the mean time it took a person to find their dream home is between 5.64 months and 6.16 months.

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