Consider a study analysing the time (hours) between receiving spam emails. A sample of 30 spam emails was recorded and the time (hours) between receiving each one. The data collected is displayed below as a histogram and boxplot. The mean of the sample is =2.80 x = 2.80 hours and the standard deviation is =0.967 s = 0.967 hour. a) Why is it important to examine data graphically? (b)Describe the shape (symmetry/modality) of the distribution for the sample. (c) Consider the received 30 spam emails, what is the chance that the average time between receiving spam emails is less than 2.5 hours? Provide a diagram to support your answer. Hint: use the t-table. (d) Calculate a 95% confidence interval for the true average of the time between receiving spam emails using the recorded sample. (e) An IT company claims the population average of time between receiving spam emails is 2.4 hours. Use part (d) to discuss briefly whether the IT company's claim is valid and state one conclusion that can be made from the confidence interval. Explain briefly. (f) If a sample of size 10 was taken from the recorded times and used as a point estimate to calculate the confidence interval for the true average, would this interval be accurate? Give reasons