In a particular experiment to see if caffeine consumption has a statistically significant effect upon memory, a student found that the caffeine consumers scored a 97 while those who didn't consume caffeine scored an 89. the student also determined that t=2.39 and p=0.03. what can the student conclude? (a) there is not a statistically significant difference in scores between these two groups based solely on the high t-value(b) there is a statistically significant difference in scores between these two groups based solely on the low p-value (c) there is a statistically significant difference in scores between these two groups based solely on the large difference in means(d) not enough information is given(e) there is a statistically significant difference in scores between these two groups based solely on the high p-value

the correct answer is (B) There is a statistically significant difference in scores between these two groups based solely on the low p-value

Step-by-step explanation:

The p-value is the level of marginal significance within a statistical hypothesis test representing the probability of the occurrence of a given event. The p-value is used as an alternative to rejection points to provide the smallest level of significance at which the null hypothesis would be rejected. In this case the  small p-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis, so you reject the null hypothesis. A large p-value (> 0.05) indicates weak evidence against the null hypothesis, so you fail to reject the null hypothesis.

The slopes are the opposite and reciprocal

Step-by-step explanation:

The Slope of a Line

Suppose we know the line passes through points A(x1,y1) and B(x2,y2). The slope can be calculated with the equation:

We need to prove lines RS and VU of the figure have the opposite and reciprocal slope, i.e., the lines are perpendicular.

Finding the coordinates of the points from the image:

R=(-2,5) S=(-5,2) V=(5,2) U=(2,5)

The slope of the line RS is:

The slope of line VU is:

Since:

The slopes are the opposite and reciprocal