Data presentation and interpretation

The times, x minutes, taken by 40 people to complete a puzzle are summarised by Σ x = 1520, Σ x² = 59 600. (a) Find the mean and standard deviation. (b) An outlier is defined as a value more than 2 standard deviations from the mean. Determine whether a time of 53 minutes is an outlier.

A student collects data on daily hours of sunshine and the number of ice creams sold at a kiosk on 12 randomly chosen days. The product moment correlation coefficient is r = -0.62. (a) Test, at the 5% significance level, whether there is evidence of correlation between hours of sunshine and ice cream sales. (Critical value for a two-tailed test at 5% with n = 12: 0.5760.) (b) The student says this proves that sunshine reduces ice cream sales. Comment on this claim. (c) The critical value for a two-tailed test at 1% with n = 12 is 0.7079. State, with a reason, whether your conclusion would change at the 1% level.