Nina can ride her bike 63,360 feet in 3,400 seconds, and Sophia can ride her bike 10 miles in 1 hour. What is Nina's
2 answers:
You might be interested in
Answer:
Bias for the estimator = -0.56
Mean Square Error for the estimator = 6.6311
Step-by-step explanation:
Given - A normally distributed random variable with mean 4.5 and standard deviation 7.6 is sampled to get two independent values, X1 and X2. The mean is estimated using the formula (3X1 + 4X2)/8.
To find - Determine the bias and the mean squared error for this estimator of the mean.
Proof -
Let us denote
X be a random variable such that X ~ N(mean = 4.5, SD = 7.6)
Now,
An estimate of mean, μ is suggested as
Now
Bias for the estimator = E(μ bar) - μ
=
=
=
=
=
= 3.9375 - 4.5
= - 0.5625 ≈ -0.56
∴ we get
Bias for the estimator = -0.56
Now,
Mean Square Error for the estimator = E[(μ bar - μ)²]
= Var(μ bar) + [Bias(μ bar, μ)]²
=
=
=
=
=
=
=
= 6.6311
∴ we get
Mean Square Error for the estimator = 6.6311
Answer:
The statistic for this case would be:
And replacing we got:
Step-by-step explanation:
For this case we have the following info:
represent the sample size
represent the number of employees that earn more than 50000
We want to test the following hypothesis:
Nul hyp.
Alternative hyp :
The statistic for this case would be:
And replacing we got:
And the p value would be given by:
if 4 pound bag = $ 12.16
1 pound bag = ?
= $3.15