Multiple Choice
Which of the following must be true for an estimator of a population parameter to be unbiased?
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7. Sampling Distributions & Confidence Intervals: Mean
Introduction to Confidence Intervals
Multiple Choice
In the context of the widget cost regression model, what does the -value associated with the statistic indicate?
A
It indicates the proportion of variance in widget cost explained by the model.
B
It measures the probability that the residuals are normally distributed.
C
It tests whether at least one predictor variable in the model has a statistically significant relationship with the response variable.
D
It gives the likelihood that the slope of the regression line is exactly .
Verified step by step guidance1
Understand that the F statistic in a regression model is used to test the overall significance of the model, specifically whether the model explains a significant amount of variation in the response variable compared to a model with no predictors.
Recognize that the p-value associated with the F statistic represents the probability of observing an F value as extreme as, or more extreme than, the one calculated from the sample data, assuming the null hypothesis is true.
Recall that the null hypothesis for the F test in regression states that all regression coefficients (except the intercept) are equal to zero, meaning none of the predictor variables have a linear relationship with the response variable.
Interpret the p-value: a small p-value (typically less than 0.05) indicates strong evidence against the null hypothesis, suggesting that at least one predictor variable is significantly related to the response variable.
Note that this p-value does not measure the proportion of variance explained, the normality of residuals, or the likelihood that a single slope coefficient is zero; it specifically tests the overall significance of the regression model.
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