STT 101 Descriptive Statistics and Statistical Inference Assignment Topics: Chi-Square Test of Independence 1. (Spam and attachments). Modern e-mail servers and anti-spam filters attempt to identify spam e-mails and direct them to a junk folder. There are various ways to detect spam, and research still continues. In this regard, an information security officer tries to confirm that the chance for an e-mail to be spam depends on whether it contains images or not. The following data were collected on n = 1000 random e-mail messages, With Images No Images Row Total Spam 160 240 400 No Spam 140 460 600 Column Total 300 700 1000 Test the hypothesis that being spam and containing images are independent at 0.05 level of significance. 2. (Internet shopping on different days of the week). A web designer suspects that the chance for an internet shopper to make a purchase through her web site varies depending on the day of the week. To test this claim, she collects data during one week. when the web site recorded 3758 hits. Observed Mon The Wed Thu Fri Sat Sun | Total No purchase 261 284 263 393 531 502 2633 Single purchase 119 72 51 143 145 150 717 Multiple purchases 39 15 41 97 348 Total 567 383 401 329 577 773 738 3768 Test the hypothesis that making a purchase or multiple purchases is independent on the day of the week. Use a = 0.01