C955 Applied Probability and Statistics - Set 5 - Part 2

Correct Answer: Fail to reject the null hypothesis

Since 0.12 exceeds 0.05, there is insufficient evidence to reject the null hypothesis, so we fail to reject it.

Correct Answer: Stronger evidence against it

A smaller p-value means the observed data would be more surprising if the null hypothesis were true, providing stronger evidence against it.

Correct Answer: The data do not provide enough evidence to conclude an effect exists

Failing to reject means the evidence is insufficient to conclude an effect, which is not the same as proving no effect exists.

Correct Answer: It decreases

The significance level is the Type I error rate, so lowering it to 0.01 reduces the probability of falsely rejecting a true null hypothesis.

Correct Answer: The Type II error rate tends to increase

Making rejection harder reduces false positives but makes it more likely to miss a real effect, increasing the Type II error rate unless the sample is enlarged.

Correct Answer: Strong negative linear relationship

The negative sign indicates an inverse relationship, and the magnitude 0.85 is close to 1, indicating a strong linear association.

Correct Answer: A weak linear relationship

A value near zero indicates little linear association, so 0.10 reflects a weak positive linear relationship.

Correct Answer: 0.36

The coefficient of determination is r squared: 0.6 squared equals 0.36, meaning about 36 percent of the variation is explained by the model.

Correct Answer: 36% of the variation in the response is explained by the model

R squared gives the proportion of variance in the response explained by the predictor, so 0.36 means the model accounts for 36 percent of the variation.

Correct Answer: y increases by 2 for each one-unit increase in x

The slope is the predicted change in y per one-unit increase in x, so here y rises by 2 for every unit increase in x.

Correct Answer: 11

Substituting x equals 4 gives 3 plus 2 times 4, which is 3 plus 8, equaling 11.

Correct Answer: The predicted value of y when x is zero

The intercept is the predicted response when the predictor equals zero, provided zero is meaningful and within the data range.

Correct Answer: A false alarm indicating an effect that is not real

A Type I error is a false positive: concluding that an effect exists when it actually does not, analogous to a false alarm.

Correct Answer: A missed detection of a real effect

A Type II error is a false negative: failing to detect an effect that genuinely exists, analogous to a missed detection.

Correct Answer: Cluster sampling

Cluster sampling randomly selects whole naturally occurring groups, such as schools or city blocks, and studies all members of the chosen clusters, often for practical efficiency.

Correct Answer: Selecting every kth member from an ordered list after a random start

Systematic sampling picks every kth element from a list after a random starting point, which is simple but can be biased if the list has a periodic pattern.

Correct Answer: It ensures representation of important subgroups and can improve precision

By sampling within each stratum, stratified sampling guarantees subgroups are represented and often yields more precise estimates than simple random sampling.

Correct Answer: It reduces sampling variability and produces more precise estimates

Larger samples reduce the standard error, producing more precise estimates, though they do not correct bias arising from a flawed sampling method.

Correct Answer: Yes, if the sampling method is biased

Sample size does not fix bias. A large but non-representative sample, such as a huge self-selected survey, can be confidently wrong.

Correct Answer: Nothing directly; significance and magnitude are separate

Significance indicates whether an effect is detectable given the data, but says nothing about its magnitude, which requires an effect size measure.