Draw back-to-back stem-and-leaf diagram

6 Employees at a particular company have been working seven hours each day, from 9 am to 4 pm . To try to reduce absence, the company decides to introduce 'flexi-time' and allow employees to work their seven hours each day at any time between 7 am and 9 pm . For a random sample of 10 employees, the numbers of hours of absence in the year before and the year after the introduction of flexi-time are given in the following table. Use a paired sample \(t\)-test to test, at the \(10 \%\) significance level, whether the population mean number of hours of absence has decreased, following the introduction of flexi-time.

10 Customers were asked which of three brands of coffee, \(A , B\) and \(C\), they prefer. For a random sample of 80 male customers and 60 female customers, the numbers preferring each brand are shown in the following table. Test, at the \(5 \%\) significance level, whether there is a difference between coffee preferences of male and female customers. A larger random sample is now taken. It consists of \(80 n\) male customers and \(60 n\) female customers, where \(n\) is a positive integer. It is found that the proportions choosing each brand are identical to those in the smaller sample. Find the least value of \(n\) that would lead to a different conclusion for the 5\% significance level hypothesis test.

4 The times taken, in seconds, by 15 members of each of two swimming clubs, the Penguins and the Dolphins, to swim 50 metres are shown in the following table.

1. Draw a back-to-back stem-and-leaf diagram to represent this information, with Penguins on the left-hand side. \includegraphics[max width=\textwidth, alt={}, center]{9b21cc0f-b043-4251-8aa9-cb1e5c2fb5d0-09_2720_33_141_20} The diagram shows a box-and-whisker plot representing the times for the Penguins.
2. On the same diagram, draw a box-and-whisker plot to represent the times for the Dolphins. \includegraphics[max width=\textwidth, alt={}, center]{9b21cc0f-b043-4251-8aa9-cb1e5c2fb5d0-09_719_1219_424_424}
3. Hence state one difference between the distributions of the times for the Penguins and the Dolphins.

6 The weights, in kg, of 15 rugby players in the Rebels club and 15 soccer players in the Sharks club are shown below.

1. Represent the data by drawing a back-to-back stem-and-leaf diagram with Rebels on the left-hand side of the diagram.
2. Find the median and the interquartile range for the Rebels.
   A box-and-whisker plot for the Sharks is shown below. \includegraphics[max width=\textwidth, alt={}, center]{a2709c37-6e81-4873-8f38-94cb9f3c3252-09_533_1246_388_445}
3. On the same diagram, draw a box-and-whisker plot for the Rebels.
4. Make one comparison between the weights of the players in the Rebels club and the weights of the players in the Sharks club.

4 The lengths of time in minutes to swim a certain distance by the members of a class of twelve 9 -year-olds and by the members of a class of eight 16 -year-olds are shown below.

1. Draw a back-to-back stem-and-leaf diagram to represent the information above.
2. A new pupil joined the 16 -year-old class and swam the distance. The mean time for the class of nine pupils was now 13.6 minutes. Find the new pupil's time to swim the distance.

1 Some adults and some children each tried to estimate, without using a watch, the number of seconds that had elapsed in a fixed time-interval. Their estimates are shown below.

1. Draw a back-to-back stem-and-leaf diagram to represent the data.
2. Make two comparisons between the estimates of the adults and the children.

5 The weights, in kg, of the 11 members of the Dolphins swimming team and the 11 members of the Sharks swimming team are shown below.

1. Draw a back-to-back stem-and-leaf diagram to represent this information, with Dolphins on the left-hand side of the diagram and Sharks on the right-hand side.
2. Find the median and interquartile range for the Dolphins.