The probability that a randomly chosen inhabitant (of any age) of a particular town is in paid employment is 0.4. A random sample of seven people is drawn from the population of the town. You may assume that the number of people in paid employment in this sample has an appropriate binomial distribution. For the questions given, select the oorrect answer (to three decimal places) from the drop-down list. What is the probability that exactly four of these people are in paid employment? What is the probability that two or fewer of these people are in paid employment? Choose... v Select from the drop-down list, the correct test to use for the given scenario. A gardener is interested in which of two different varieties of runner bean produces the highest average yield in her garden. She grows thirty plants of each of the two varieties and measures the yield of beans (in grams) from each of them. A researcher is interested in whether which of two types of woollen glove are more effective. He gets eight volunteers to wear one of the types of glove on their left hand and the other type of glove on their right hand before standing in a cold room for an hour. He then measures the temperature of each hand. You may assume that any relevant quantities come from a normal distribution. Choose... Choose... Select the TWO options that are TRUE statements about two-sample t-tests. Select one or more: The critical values for the two-sample t-test with unequal variances and the two-sample z-test, for given sample sizes, are generally different. A researcher has collected two samples of data and the sample variances are 1.45 and 2.11. It would be appropriate to use the two-sample t-test with a common variance. The same formula is used for the ESE (estimated standard error) in the two-sample t-test with a common variance and the two-sample z-test. It is not possible to find a confidence interval for the difference between two means based on the two sample t-test with unequal variances. A researcher has collected two samples of data and the sample variances are 0.34 and 2.11. It would be appropriate to use the two-sample t-test with a common variance.A hexplot of some data is as follows. Using this boxplot, answer the following questions. Does the boxplot show that the data are left-skew, symmetric or right-skew? Choose... v Approximately what percentage of the data lies between 20 and 60? Choose... v Approximately what percentage of the data lies between 0 and 60? Choose... v