Is it possible that when you fit a simple regression model, the t-statistic for the slope coefficient is large (outside the range of (-2,2)), indicating that the X variable has a linear relationship with the Y variable, but that the R-squared value is quite low, say 8%?

(i) Yes (justify your choice with a short explanation)

(ii) No (justify your choice with a short explanation)

The CLT (Central Limit Theorem) will hold for any sample size if the distribution of the individual values of the variable Y is normal to begin with (You do NOT have to provide a justification for your choice for this question)

a) True

b) False

A company wants to compute a 95% CI for the average monthly electricity consumption of their customers such that the CI has a width of 3 units. The company has an estimate of the population standard deviation of electricity consumption as 5 units. How large a sample size should they take to compute this CI?