Please help with statistics.! Thank you very much! Q 1. If a statistic used to e
ID: 3255457 • Letter: P
Question
Please help with statistics.! Thank you very much!
Q 1.
If a statistic used to estimate a parameter is such that the mean of its sampling distribution is equal to the actual value of the parameter, what is the statistic said to be?
a) a proportion
b) Random
c)Biased
d) Unbiased
e) varied
Q2
A quarterback for the Seattle Seahawks completes 54 % of his passes. Let random variable X be the number of passes completed in 20 attempts. Conduct a simulation of the 200 attempts using the following random digits. Be sure to state how you assign your digits. 98726 10983 56239 42042 76520 68276 58239 48729 84912 87491
a) What proportions of passes was completed?
b) How does this compare with what “should have happened” theoretically?
Q3
An SRS of 400 American adults is asked, "What do you think is the most serious problem facing our schools?" Suppose that in fact 30% of all adults would answer drugs if asked this question. The proportion p-hat of the sample who answer drugs will vary in repeated sampling. In fact, you can assign probabilities to values of p-hat using the normal density curve with mean 0.3 and standard deviation 0.023. Use this density curve to find the probabilities of the following events:
a) At least half of the sample believes that drugs are the schools' most serious problem.
b) Less than 25% of the sample believes that drugs are the most serious problem.
c) The sample proportion is between 0.25 and 0.35.
Explanation / Answer
Dear student, I am only answering the first question as per Chegg Guidelines.
Q 1.
If a statistic used to estimate a parameter is such that the mean of its sampling distribution is equal to the actual value of the parameter, what is the statistic said to be?
It is then called unbiased estimator as the mean is equal to the actual parameter under consideration, i.e.,
E( theta cap)=theta
So the correct answer is (d) Unbiased