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dman09082000
15.04.2020 •
Mathematics
Hannibal wants to estimate the true average brain mass, u, but he is locked in a cell with no internet and only has a scale. He collects a small random sample of size n = 5 from nearby prison guards. He find that these brains have the following weights:
1320g, 1400g, 1300g, 1460g, 1350g
Suppose that human brains follow a normal distribution, and that Hannibal's sample is representative of the entire population.
a. (1 pt) Compute the sample standard deviation, s, of these brains. Do not use a computer for part (a). You may only use +, -, X, -, and ✓ on a calculator. Show all your work.
b. (1 pt) Construct a two-sided 95% confidence interval for the true mean weight of brains, u. You may use a computer/calculator to calculate critical values, but not to solve the entire problem.
c. (1 pt) Construct a two-sided 82% confidence interval for the true mean weight of brains, u.
d. (1 pt) Construct a one-sided 95% confidence interval for the true mean weight of brains, u. Give the lower bound. Your interval will look like this: (Lower Bound, 00)
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Ответ:
a) s=64.65
b)![1309.33\leq \mu \leq 1422.67](/tpl/images/0603/0880/572a4.png)
c)![1327.26\leq \mu \leq 1404.74](/tpl/images/0603/0880/84bcc.png)
d)![\mu \geq 1318.44](/tpl/images/0603/0880/1b082.png)
Step-by-step explanation:
a) To calculate the sample standard deviation, first we have to calculate the sample mean.
Now, the standard deviation is:
b) The z-value for a 95% confidence interval is z=1.96.
The margin of error is
The lower and upper limit of the CI are:
The confidence interval is:
c) In this case, the z-value for a 82% CI is z=1.34.
The margin of error is
The lower and upper limit of the CI are:
The confidence interval is:
c) Now we have to construct a one sided 95% confidence interval, with only one bound (lower bound).
The z-value is z=1.645
The margin of error is
The lower limit of the CI is:
The confidence interval is:
Ответ:
yeet
Step-by-step explanation:
urmom