Final answer:
It is true that a large correlation can be detected as statistically significant even with a small sample size of 30 people. Statistical significance is often assessed through hypothesis testing and confidence intervals. However, larger sample sizes generally provide more accurate estimates and stronger evidence of significant correlations.
Step-by-step explanation:
The statement that 'we have a reasonable chance of detecting a large correlation as being statistically significant even if we only test 30 people' can be considered true. When dealing with a small sample size, such as 30, a strong or large correlation may still be detected as statistically significant. This is due to the fact that statistical tests like the correlation coefficient test are sensitive to the strength of the relationship between variables as well as the sample size. However, it is important to note that with small sample sizes, a correlation might also be more influenced by outliers or variations that do not represent the population accurately.
The notion that correlation does not imply causation is true. This is a fundamental concept in statistics, indicating that, even if two variables have a strong correlation, one might not be the cause of the other. Lastly, it is important to understand that in science, conclusions about correlations and their significance are drawn based on the alternate hypothesis (Ha) stating that the population correlation coefficient is significantly different from zero, which suggests there is a significant linear relationship.
Regarding confidence intervals, part c is correct by stating that if we took repeated samples, approximately 90 percent of the confidence intervals calculated from those samples would contain the true value of the population mean. This is the basic concept behind confidence intervals in hypothesis testing. It is also accurate that a normal distribution is usually a well-suited approximation when the sample size is greater than 30, as per part i of the provided information.