Question

We want to know whether an independent variable (room temperature) affects scores on a dependent variable (ratings of anger). The levels of the IV are hot and cold and the DV is measured on an anger scale (ranging from 0 no anger to 10 high anger). A random sample of subjects has been taken from the universe. Half of the subjects are randomly placed in the hot room while the other half are placed in the cold room.

The samples are said to be                              because                      subjects are responding in the hot room than are responding in the cold room.

The data:         Subject                        Hot room                     Subject                        Cold room

                              1                      5                                  11                    3

                              2                      8                                  12                    2

                              3                      5                                  13                    6

                              4                      8                                  14                    6

                              5                      9                                  15                    4

                              6                      7                                  16                    4

                              7                      2                                  17                    3

                              8                      8                                  18                    2   

                              9                      4                                  19                    2

                                    10        6          20        3

Answer 1

If there is no influence of room temperature on ratings of anger, average ratings are expected not to be significantly different.

Here we are given with two sets of sample values in two different conditions as hot temperature and cold temperature.

We do not know population standard deviation (or variance). So, we have to perform two sample t-test for equality of means.

Suppose, random variables H and C denotes ratings in hot rooms and cold rooms respectively.

We have to test for null hypothesis

against the alternative hypothesis

Our test statistic is given by

Here,

First sample size

Second sample size

Degrees of freedom

[Using R-code '1-pt(3.199308,18)+pt(-3.199308,18)']

We reject our null hypothesis if , level of significance.

We generally test for level of significance 0.10, 0.05, 0.01 or something like these.

So, we reject our null hypothesis.

Hence, based on the given data we can conclude that the room temperature affects scores of ratings in anger.

Thus the samples are said to be dependent on room temperature because theses is significant difference among subjects in responding in the hot room than are responding in the cold room.