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tatiyna
3 years ago
15

According to a recent study, the mean cost of a 3 bedroom home costs less in Ohio than in Alabama. You think this information is

incorrect. You randomly select 35 homes in each state. In Ohio, the mean cost is $137,400. In Alabama, the mean cost is $135,900. From past studies, the population standard deviation for 3 bedroom homes in Ohio is $3200 and in Alabama is $2800. Is there enough evidence to support your claim at α = 0.05?
Mathematics
1 answer:
Kobotan [32]3 years ago
3 0

Answer:Yes it is

Step-by-step explanation:

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There is a relationship between confidence interval and standard deviation:
\theta=\overline{x} \pm \frac{z\sigma}{\sqrt{n}}
Where \overline{x} is the mean, \sigma is standard deviation, and n is number of data points.
Every confidence interval has associated z value. This can be found online.
We need to find the standard deviation first: 
\sigma=\sqrt{\frac{\sum(x-\overline{x})^2}{n}
When we do all the calculations we find that:
\overline{x}=123.8\\ \sigma=11.84
Now we can find confidence intervals:
($90\%,z=1.645): \theta=123.8 \pm \frac{1.645\cdot 11.84}{\sqrt{15}}=123.8 \pm5.0\\($95\%,z=1.960): \theta=123.8 \pm \frac{1.960\cdot 11.84}{\sqrt{15}}=123.8 \pm 5.99\\ ($99\%,z=2.576): \theta=123.8 \pm \frac{2.576\cdot 11.84}{\sqrt{15}}=123.8 \pm 7.87\\
We can see that as confidence interval increases so does the error margin. Z values accociated with each confidence intreval also get bigger as confidence interval increases.
Here is the link to the spreadsheet with standard deviation calculation:
https://docs.google.com/spreadsheets/d/1pnsJIrM_lmQKAGRJvduiHzjg9mYvLgpsCqCoGYvR5Us/edit?usp=sharing
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Step-by-step explanation:

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