Probability and Statistics Assignment | homework help websites

True or False
Instructions: If the statement is true, say so. If it is false, either:
a. State the corrected statement
b. Provide a counterexample
c. Say why the statement is incorrect.
1. If the 95% confidence interval for the slope of the true regression line is (-1.44,0.199). The estimate
for is significantly different from 0.
2. Correlation implies causation.
3. A correlation coefficient of r = 0.1 implies that there is no relationship between the variables
4. A 99% confidence interval of (0,1) is interpreted as being 99% confident that the true parameter value is
in the range from 0 to 1.
5. When counting, a combination implies that order doesn’t matter. Hence, if a class of 25 elects 3 persons
to fill the positions president, treasurer and secretary, then a combination can be used to count the
number of ways this group can be formed.
6. If A and B are independent, then P(A|B)=P(B)
7. If I roll 2 dice where the event A= getting a 6 on dice 1 and event B is getting a 3 on dice 2. Events A
and B are not independent.
8. The central limit theorem states that if the sample size is large enough, then each sample is normally
distributed.
9. Failing to reject the null hypothesis in any hypothesis test means that the null hypothesis is true.
10. Power is the probability of rejecting the null hypothesis when the null hypothesis is not true
11. As the distance between the null mean and the true mean decreases, the power increases.
12. A simple random sample is not truly random.
13. There are 2 methods we learnt in this class to make an inference: Hypothesis testing and Confidence
intervals. We use a Hypothesis test when we have prior information about the population.
14. To find an MVUE, we find the estimator that is unbiased, has minimum variance and is in the lower
percentile.
Multiple Choice
Instructions: Provide some justification as to why you chose a specific answer.
15. Which of the following statements are not correct?
a) The coefficient of determination, denoted by is interpreted as the
proportion of observed y variation that cannot be explained by the simple
linear regression model.
b) The higher the value of the coefficient of determination, the more
successful is the simple linear regression model in explaining y variation.
c) If the coefficient of determination is small, an analyst will usually want to
search for an alternative model (either a nonlinear model or a multiple
regression model that involves more than a single independent variable).
d) All of the above statements are correct.
16. In testing, t
check this probability?
a) Geometric distribution
b) Binomial Distribution
c) Hypergeometric distribution
d) Poisson distribution
e) None of the above