Question

1. Tide Pods are concentrated laundry detergent packets, which have been sold since 2012. Their colorful appearance and small size have led to nearly 7,700 pod-related calls to poison centers for children under 5. In 2017, a series of memes featured Tide Pods as “forbidden fruit.” In January 2018 a (mostly) satirical Tide Pod Challenge appeared, that “encouraged” teenagers to eat tide pods, video the experience, and post it online.
   1. During the first 30 days of 2018, there were 93 calls to poison control centers for teenagers who intentionally ate laundry pods. Typically, the number of calls for teenagers ingesting laundry pods in a month has  = 37 and s = 12. What is the z-score for number of calls in January 2018? What does this imply?
   2. Public was associating increased sharing/view rate of videos tagged “Tide Pod Challenge” with increased calls to poison control centers for eating Tide Pods? For each day in the first 30 days of 2018, the number of YouTube views and poison center calls were measured.  The correlation was r = .41. Is this a significant correlation at the 95% confidence level? Should YouTube take the videos down?
   3. In response to the Tide Pod Challenge, P&G has added warnings about ingesting laundry pods. This may have reduced poisoning incidents involving children. Based on data from the first 15 weeks of 2018, weekly calls for children had an average of 119 and std. deviation of 20. Data from before 2018 had weekly calls of at least 148. Has the number of poisoning incidents decreased? Write the null and alternative hypothesis.
   4. Calculate the test statistic, and with 95% confidence, state your conclusion.

Answer 1

a. As, Z = (x - ) / , Z = (93 - 37)/12 = 4.666667 . Z-score says by how many standard deviations the data point is far from mean. Here Z-score says that 93 is ~5 standard deviations far from observed mean i.e., the value is not close to mean.

b.

r = 0.41 says that YouTube views have a moderately linear relationship with poison center calls i.e., not all the variance in YouTube views is not being explained by calls. Since, it is significant positive correlation, taking down YouTube videos may show a decrease in poison center calls.

c. Since monthly calls in 2017 is at least is 148. So average will be greater than or equal to 148 for 2017. But the values in 2018, will range from 99 to 139 (according to first standard deviation), which are less than average in 2017. So this says that poisoning incidents have been decreased.

Ho:mu >= 148

Ha: mu < 148

d)