# mathematics

1. Compute four-week and five-week moving averages for the time series (to 2 decimals).
Four week
Five Week

b. Compute the MSE for the four-week and five-week moving average forecasts (to 2 decimals).

MSE (4 week)
MSE (5 week)

b. What appears to be the best number of weeks of past data (three, four, or five) to use in the moving average computation? Recall that MSE for the three-week moving average is 10.22.
Select one of the following:
The 3-week moving average provides the smallest MSE
The 4-week moving average provides the smallest MSE
The 5-week moving average provides the smallest MSE

show the exponential smoothing forecasts using = 0.1.

A) Applying the MSE measure of forecast accuracy, would you prefer a smoothing constant of = .1 or = .2 for the gasoline sales time series (to 2 decimals)?
MSE for = .1 __________
MSE for = .2___________

B) Are the results the same if you apply MAE as the measure of accuracy (to 2 decimals)?
MAE for = .1_________
MAE for = .2_________

C) What are the results if MAPE is used (to 2 decimals)?

MAE for = .1_________
MAE for = .2_________

• question.docx
 1. If n=15 and p=0.4, then the standard deviation of the binomial distribution is 3.6. (Ch6)(Points : 8)

True
False

 Question 2.2. If the level of confidence and sample size remain the same, a confidence interval for a population proportion p will be narrower when p(1-p) is larger than when it is smaller. (Ch9) (Points : 8)

True
False

 Question 3.3. In a simple linear regression model, the coefficient of determination not only indicates the strength of the relationship between independent and dependent variable, but also shows whether the relationship is positive or negative. (Ch13) (Points : 8)

True
False

 Question 4.4. The sample standard deviation s is an unbiased estimator of the population standard deviation. (Ch8) (Points : 8)

True
False

 Question 5.5. If the random variable of x is normally distributed, 68.26% of all possible observed values of x will be within two standard deviations of the mean. (Ch7) (Points : 8)

True
False

 Question 6.6. If n=20 and p=.4, then the mean of the binomial distribution is 8 (Ch6) (Points : 8)

True
False

 Question 7.7. First a confidence interval is constructed without using the finite population correction factor. Then, for the same identical data, a confidence interval is constructed using the finite population correction factor. The width of the interval with the finite population correction factor is wider than the confidence interval without the finite population correction factor. (Ch9) (Points : 8)

True
False

 Question 8.8. The power of a statistical test is the probability of rejecting the null hypothesis when it is true. (Ch10) (Points : 8)

True
False

 Question 9.9. The sampling distribution of the sample mean is developed by repeatedly taking samples of size n and computing the sample means and reporting the resulting sample means in the form of a probability distribution. (Ch8) (Points : 8)

True
False

 Question 10.10. For a continuous distribution, the exact probability of a particular value is always zero. (Ch7) (Points : 8)

True
False

 Question 11.11. As the level of significance a increases, we are more likely to reject the null hypothesis. (Ch10) (Points : 8)

True
False

 Question 12.12. If events A and B are mutually exclusive, then P(A|B) is always equal to zero. (Ch5) (Points : 8)

True
False

 1. If n=15 and p=0.4, then the standard deviation of the binomial distribution is 3.6. (Ch6)(Points : 8)

True
False

 Question 2.2. If the level of confidence and sample size remain the same, a confidence interval for a population proportion p will be narrower when p(1-p) is larger than when it is smaller. (Ch9) (Points : 8)

True
False

 Question 3.3. In a simple linear regression model, the coefficient of determination not only indicates the strength of the relationship between independent and dependent variable, but also shows whether the relationship is positive or negative. (Ch13) (Points : 8)

True
False

 Question 4.4. The sample standard deviation s is an unbiased estimator of the population standard deviation. (Ch8) (Points : 8)

True
False

 Question 5.5. If the random variable of x is normally distributed, 68.26% of all possible observed values of x will be within two standard deviations of the mean. (Ch7) (Points : 8)

True
False

 Question 6.6. If n=20 and p=.4, then the mean of the binomial distribution is 8 (Ch6) (Points : 8)

True
False

 Question 7.7. First a confidence interval is constructed without using the finite population correction factor. Then, for the same identical data, a confidence interval is constructed using the finite population correction factor. The width of the interval with the finite population correction factor is wider than the confidence interval without the finite population correction factor. (Ch9) (Points : 8)

True
False

 Question 8.8. The power of a statistical test is the probability of rejecting the null hypothesis when it is true. (Ch10) (Points : 8)

True
False

 Question 9.9. The sampling distribution of the sample mean is developed by repeatedly taking samples of size n and computing the sample means and reporting the resulting sample means in the form of a probability distribution. (Ch8) (Points : 8)

True
False

 Question 10.10. For a continuous distribution, the exact probability of a particular value is always zero. (Ch7) (Points : 8)

True
False

 Question 11.11. As the level of significance a increases, we are more likely to reject the null hypothesis. (Ch10) (Points : 8)

True
False

 Question 12.12. If events A and B are mutually exclusive, then P(A|B) is always equal to zero. (Ch5) (Points : 8)

True
False

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