Determine the next three terms in the following sentence 2, 3, 5, 8, _, _, _
2 answers:
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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 probability of rejecting the null hypothesis, when it is true, is 5%.
Step-by-step explanation:
We know that the level of significance ( denoted as ) is generally the probability of rejecting the null hypothesis when it is true.
Therefore , If the level of significance (\alpha[/tex] ) 0.05, then it means that it is the probability of rejecting the null hypothesis when it is true.
i.e. The probability of rejecting the null hypothesis when it is true= 0.05
In percent :
Hence, the correct option is : The probability of rejecting the null hypothesis when it is true is 5%.