In exponential smoothing, a higher value of the smoothing parameter (alpha) gives _______ weight to recent observations.
Higher
Lower
Zero
Equal
An autoregressive model (AR) uses ______ values of the time series to predict future values.
Future
Random
Past
Average
What is a Type II error in hypothesis testing?
Incorrectly calculating the p-value.
Rejecting the null hypothesis when it is true.
Using the wrong test statistic for the data.
Failing to reject the null hypothesis when it is false.
An event has three possible outcomes: A, B, and C. You know P(A) = 0.2 and P(B) = 0.3. What is the value of P(C) according to the law of total probability?
0.5
Cannot be determined
0.3
0.7
You want to compare the average heights of men and women in a population. Which hypothesis test would be most appropriate?
Chi-square test
Independent samples t-test
One-sample t-test
Paired t-test
Which of the following is NOT an assumption of a t-test?
The data is categorical.
The data is normally distributed.
The observations are independent.
The variances of the groups being compared are equal (for independent samples t-test).
A 95% confidence interval for a population mean is calculated to be (60, 80). What is the correct interpretation of this interval?
If we were to repeatedly construct confidence intervals using this method, 95% of them would contain the true population mean.
If we were to repeatedly sample from this population, 95% of the time the sample mean would fall between 60 and 80.
There is a 95% probability that the true population mean falls between 60 and 80.
We are 95% confident that the sample mean falls between 60 and 80.
What is the primary difference between simple exponential smoothing and double exponential smoothing?
Double exponential smoothing is used for stationary data, while simple exponential smoothing is used for non-stationary data.
Simple exponential smoothing considers seasonality, while double exponential smoothing does not.
Double exponential smoothing considers trend, while simple exponential smoothing does not.
Simple exponential smoothing uses a moving average, while double exponential smoothing uses an autoregressive model.
A company manufactures light bulbs. The probability that a bulb is defective is 0.05. If you choose 3 bulbs at random, what is the probability that at least one bulb is defective?
0.857
0.000125
0.143
0.999875
In simple linear regression, what does a negative slope of the regression line indicate?
The relationship between the independent and dependent variables is non-linear.
As the independent variable increases, the dependent variable decreases.
As the independent variable increases, the dependent variable increases.
There is no relationship between the independent and dependent variables.