Testing correlationsWe wish to test if there is sufficient evidence that weight and intelligence are correlated.Ordinary correlationWe can begin by using the t-test:T = ˆρij√ n − 21 − ˆρ2ij= 0.6162√ n − 21 − 0.61622 = 3.3193872.The t distribution has n − 2 degrees of freedom

Recall the 3-variable example from before:1. X1: Intelligence2. X2: Weight3. X3: AgeSuppose that these correlations are actually based on sample size n = 20:ˆρ = 1 0.6162 0.82670.6162 1 0.73210.8267 0.7321 1

Past experience has shown that scores on a particular skills-based test (A) are distributed Normally (mean=25, std=8) and scores on an alternative skills-based test (B) are distributed Normally (mean=30, std=6).The correlation (r) between the two test scores is zero. Which of the follwing statements is FALSE?Group of answer choicesThe two tests must be testing unrelated skills.Let T= total score for a randomly selected individual: T = A + B. It is expected that approximately 95% of total scores (T) will be between 35 and 75.There is insufficient information available to determine if A and B are independent (i.e. insufficient information to determine if scores on one test affect an individuals score on the other test.)Total score (T=A + B) can reasonably be modelled using a normal distribution.Approximately 90% of the total scores (T) are below 67.8.

The correlation coefficient between the age of a person and their IQ test score is found to be -1.0087.What can you conclude from this?Age is a good predictor of IQAge is not a good predictor of IQNone of the above

If two populations are independent and each normally distributed and the population standard deviations are not equal, the test statisticT=X¯1−X¯2−(μ1−μ2)S21n1+S22n2‾‾‾‾‾‾‾‾√𝑇=𝑋¯1−𝑋¯2−(𝜇1−𝜇2)𝑆12𝑛1+𝑆22𝑛2 follows a:Question 4Select one:a.t-distribution with n1+n2−2 degrees of freedomt-distribution with 𝑛1+𝑛2−2 degrees of freedom b.standard normal distribution with n1+n2−2 degrees of freedomstandard normal distribution with 𝑛1+𝑛2−2 degrees of freedom c.t-distribution with degrees of freedom equal to (S21n1+S22n2)2(S21/n1)2n1−1+(S22/n2)2n2−1t-distribution with degrees of freedom equal to (𝑆12𝑛1+𝑆22𝑛2)2(𝑆12/𝑛1)2𝑛1−1+(𝑆22/𝑛2)2𝑛2−1 d.t-distribution with n−1 degrees of freedom

A researcher is interested in student characteristics based on their degree programme. As part of her study, she investigates whether psychology and maths students are equally likely to have been to a bar over the previous weekend. Her survey provides the frequency of going to a bar or not going to a bar for a sample of 90 psychology students and 90 maths students. What type of test can she carry out on the data?Question 8Answera.Chi-Square Testb.McNemar Testc.Independent Sample T-Testd.Pearson's correlation