DDT is a pesticide banned in Australia for its danger to humans and animals. In an experiment on the impact of DDT, six rats were exposed to DDT poisoning and six rats were not. For each rat in the experiment, a measurement of nerve sensitivity was recorded. The researchers suspected that the mean nerve sensitivity for rats exposed to DDT is greater than that for rats not poisoned. The following data was obtained:

Let 1 be the mean nerve sensitivity for rats poisoned with DDT. Let 2 be the mean nerve sensitivity for rats not poisoned with DDT.

DDT is a pesticide banned in Australia for its danger to humans and animals. In an experiment on the impact of DDT, six rats were exposed to DDT poisoning and six rats were not. For each rat in the experiment, a measurement of nerve sensitivity was recorded. The researchers suspected that the mean nerve sensitivity for rats exposed to DDT is greater than that for rats not poisoned. The following data was obtained:

Let 1 be the mean nerve sensitivity for rats poisoned with DDT. Let 2 be the mean nerve sensitivity for rats not poisoned with DDT.

Is there a difference in the amount of airborne bacteria between carpeted and uncarpeted rooms? In an experiment, five rooms were carpeted and five were left uncarpeted. The rooms are similar in size and function. After a suitable period of time, the concentration of bacteria in the air was measured (in units of bacteria per cubic foot) in all of these rooms. The data and summaries are provided:

DDT is a pesticide banned in Australia for its danger to humans and animals. In an experiment on the impact of DDT, six rats were exposed to DDT poisoning and six rats were not. For each rat in the experiment, a measurement of nerve sensitivity was recorded. The researchers suspected that the mean nerve sensitivity for rats exposed to DDT is greater than that for rats not poisoned. The following data was obtained:

Let 1 be the mean nerve sensitivity for rats poisoned with DDT. Let 2 be the mean nerve sensitivity for rats not poisoned with DDT.

Is there a difference in the amount of airborne bacteria between carpeted and uncarpeted rooms? In an experiment, five rooms were carpeted and five were left uncarpeted. The rooms are similar in size and function. After a suitable period of time, the concentration of bacteria in the air was measured (in units of bacteria per cubic metre) in all of these rooms. The data and summaries are provided:

A psychologist has developed a set of activities that is intended to help children develop better reading skills. In a study of the effectiveness of these activities, one class of second-grade children learns with the activities. Another class of second-grade children serves as the control and learns without the activities. After some period of time, the reading skills of all of these children were assessed. A summary of these data is:

The psychologist suspects that children who learn with activities have higher mean reading skill test scores than children that don't learn with activities and decides to conduct a relevant test of significance. 

A sports writer wished to see if a football filled with helium travels farther, on average, than a football filled with air. To test this, the writer used 18 adult male volunteers. These volunteers were randomly divided into two groups of nine subjects each. Group 1 kicked a football filled with helium to the recommended pressure. Group 2 kicked a football filled with air to the recommended pressure. The mean distance for group 1 was 30 metres, with a standard deviation s_1 = 8 metres. The mean distance for group 2 was 26 metres, with a standard deviation s_2 = 6 metres. Assume the two groups of kicks are independent. Let \mu_1 and \mu_2 represent the mean distance we would observe for the entire population represented by the volunteers if all members of this population kicked, respectively, a helium- and an air-filled football. Assume that two-sample t-procedures are safe to use.