In exponential smoothing, a higher value of the smoothing parameter (alpha) gives _______ weight to recent observations.
Zero
Higher
Equal
Lower
When is it appropriate to use a one-tailed hypothesis test?
When you want to test for a difference in either direction.
When the sample size is small.
When you are only interested in detecting a difference in one direction.
When the data is not normally distributed.
A researcher wants to determine if a new drug reduces blood pressure more effectively than a placebo. They measure the blood pressure of the same group of patients before and after taking the drug and placebo (in random order). What test should they use?
Paired t-test
Independent samples t-test
One-sample t-test
ANOVA
A random variable X has the following probability distribution: P(X=0) = 0.2, P(X=1) = 0.3, P(X=2) = 0.5. What is the expected value of X?
1.5
0.5
1
1.2
Which of the following is an example of a non-parametric inferential statistical test?
Chi-square test
z-test
t-test
What pattern in residual analysis might suggest that a linear model is not appropriate for the data?
All residuals clustered around zero
Residuals consistently increasing with increasing values of the independent variable
A curved pattern in the residuals
Randomly scattered residuals
What does a p-value less than the significance level (alpha) indicate?
There is insufficient evidence to reject the null hypothesis.
There is strong evidence to reject the null hypothesis.
The alternative hypothesis is proven true.
The null hypothesis should be accepted.
A Chi-square test is used to:
Determine if a sample mean is significantly different from a known population mean.
Analyze the variance within and between groups.
Compare the means of two groups.
Analyze the relationship between two categorical variables.
As the sample size increases, the standard error of the mean:
Increases
Stays the same
Cannot be determined
Decreases
Which component of a time series reflects long-term changes in the data over time?
Trend
Irregularity
Seasonality
Cyclical Variation