Normal Distribution With Parameters - Statistics Assignment Help

Assignment Task:

Task:

1. In a normal distribution with parameters mu (mean) = -1300 and sigma (standard deviation) = 200, which of the following values is more plausible?
Select one:
a.50.
b.1300.
c.-3000.
d.0.

2. Which of the following statements is correct regarding the sampling distribution of the statistic b1?
Select one:
a.It is a probability distribution for possible values of Y.
b.It is a probability distribution for possible values of X.
c.It is a probability distribution for possible values of the mean of X.
d.It is a probability distribution for possible values of b1.

3. Which of the following statements is true about a prior distribution over possible parameter values?
Select one:

a.It represents the credence the researcher gives to possible parameter values before observing the new data.
b.It represents a null hypothesis, not an alternative hypothesis.
c.It represents the credence the researcher gives to possible parameter values after observing the new data.
d.It represents a sampling distribution of the parameter values.

4. A cognitive psychologist measured working memory capacity in humans of the same age and gender. Which of the following is a variable in the context of this study?
Select one:
a.Age.
b.Gender.
c.Working memory capacity.
d.Species.

5. In a random experiment the possible outcomes are 4, 5, 6, 7, and 8. In one of the following combinations of events A and B in the sample space, the sum of the probabilities of the events is not necessarily 1. In which one?
Select one:
a.Event A: (4,6,8), Event B: (5,7).
b.Event A: odd numbers, Event B: (4,5,6,8).
c.Event A: (4,5), Event B: (6,7,8).
d.Event A: odd numbers, Event B: even numbers.

6. In a DAG, variable R affects variable S and variable R also affects variable T. How is variable R called?
Select one:
a.A confounding variable.
b.A collider.
c.A common cause of S and T.
d.A common effect of S and T.

7. In a linear model Y = B0 + B1 X, with B0 = 50 and B1 = 10, what is the expected value for Y when X = 0?
Select one:
a.50.
b.0.
c.60.
d.10.

8. The Bayes factor (BF10) comparing the alternative hypothesis and the null hypothesis is 0.001.
Which of the following statements is correct? Select one:
a.The data is 1000 times more likely under than alternative hypothesis than under the null
hypothesis.
b.The corresponding BF01 would be 0.001.
c.The corresponding BF01 would be 10.

d.The data is 1000 times more likely under than null hypothesis than under the alternative hypothesis.

9. Which of the following statements is true about a posterior distribution over possible parameter values:
Select one:
a.It represents the credence the researcher gives to possible parameter values before observing the
new data.
b.It represents a null hypothesis, not an alternative hypothesis.
c.It represents a sampling distribution of the parameter values.
d.It represents the credence the researcher gives to possible parameter values after observing the new data.

10. The probability of the data under the alternative hypothesis is 0.0016 and that of the null hypothesis is 0.2. What is the value of the Bayes Factor (BF01)?
Select one:
a.0.008.
b.0.2.
c.125.
d.0.0016.

11. In a study, the Bayes Factor (BF10) comparing an alternative hypothesis to a null hypothesis is 0.02. Which of the following statements is correct?
Select one:
a.The data is 0.02 times more likely under the null hypothesis than under the alternative hypothesis.
b.The data is 50 times more likely under the null hypothesis than under the alternative hypothesis.
c.The data is statistically significant.
d.The posterior distribution of the alternative hypothesis is 0.02.

12. Consider the linear model Y ~ Normal (gamma, sigma), where gamma = B0 + B1 X, and the best estimates are B0 = 53 and B1 = 1.5. Consider the values X = 15 and X = 30. Which of the following pair of values of Y are more plausible?
Select one:
a.Y = 0 for X = 15, and Y = 1 for X = 30.

b.Y = 53 for X = 15, and Y = 1.5 for X = 30.
c.Y = 75 for X = 15, and Y = 100 for X = 30.
d.Y = 15 for X = 15, and Y = 30 for X = 30.

13. Which of the following statements best describes the concept of overfitting?
Select one:
a.Fitting the model to the process of interest and not to a random process.
b.Providing a bad fit of the model to the current data.
c.Using less parameters than necessary to fit the data.
d.Fitting the model to the process of interest and to a random process.

14. The probability of the data under the alternative hypothesis is 0.004 and that of the null hypothesis is 0.0001. What is the value of the Bayes Factor (BF10)?
Select one:
a.0.004.
b.0.025.
c.40.
d.0.0001.

15. In the Bayesian model comparison approach, which of the following is a characteristic of the model for the null hypothesis?
Select one:
a.A spike on the value 0.
b.A continuous uniform distribution with a mean of 0.
c.A normal distribution with a mean of 0.
d.A Beta distribution with a mean of 0.

16. In a Binomial distribution with parameters pi = 0.8 and n = 20, which of the following outcomes is more plausible?
Select one:
a.0.8 successful trials.
b.Seventeen successful trials.

c.Twenty successful trials.
d.Eight successful trials.

17. In a linear model in which the expected value for Y is 300, which of the following statements is more accurate regarding a prediction for Y.
Select one:
a.Y will be 300 or a value close to 300.
b.Y will be exactly 300.
c.Y will be higher than 300.
d.Y will be lower than 300.

18. In the null hypothesis testing approach, if the value of the statistic calculated in the sample (e.g.,
b1), or more extreme values, has a probability of 0.04, and the significance threshold chosen was 0.05, what is the correct decision?
Select one:
a.To reject the null hypothesis.
b.To reject the p value.
c.To accept the null hypothesis.
d.To reject the alternative hypothesis.

19. Why is overfitting a problem? Because the overfitting model...
Select one:
a.Will do a bad job at predicting future data.
b.Will do a great job at predicting future data.
c.Does not predict the current data very well.
d.Is a linear model.

20. An organisational psychologist is investigating worker's preferences for incentives. He asked 272 participants whether they prefer a) bonus, b) salary increase, or c) extra holidays. Based on this information, the researcher created a probability distribution of the preferences of the participants.
Which of the following cases is NOT a possible probability distribution? Select one:
a.Bonus: 0.2, Salary increase: 0.4, Extra holidays: 0.2

b.Bonus: 0.4, Salary increase: 0.5, Extra holidays: 0.1
c.Bonus: 0.8, Salary increase: 0.2, Extra holidays: 0
d.Bonus: 0, Salary increase: 0, Extra holidays:1

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