Students recruited at the cafeteria at Hope College were blindly given a single Skittles® candy to put in their mouth. They were told the five possible flavors and then were asked which flavor they had. Of the 154 healthy students tested, 78 gave the correct answer. Of the 118 students tested who had stuffy or runny noses, 44 gave the correct answer. 1. Did the study involve random sampling, random assignment, both, or neither?
2. An appropriate analysis of the data shows that there is strong evidence that healthy students were more likely to give the correct answer. Is it appropriate to conclude that the health of the student affects ability to taste? Why or why not?

1) both

2) Yes. It is appropriate to conclude that the health of the student affects ability to taste.

Step-by-step explanation:

Random Sampling  is done when each element of the sample has equal probability of being chosen. In both the samples of healthy and runny nose students each student has equal probability of being tested.

Random Assignment is one in which there is a control group and experimental group. The control group contains all the participants and each participant has the equal probability of being placed in the experimental group. For example in this experiment each student has equal probability of being tested with the given chocolate bar.

2) Yes. It is appropriate to conclude that the health of the student affects ability to taste.

the probability of success in healthy student is 78/154= 0.5065 = 50.65%

the probability of success in runny nose student is 44/118= 0.3729 = 37.29%

From this we see the probability of success is more in healthy students as compared to runny nose students

50.65> 37.29

Therefore it is appropriate to conclude that the health of the student affects ability to taste.

step-by-step explanation:

30% of $420 is 0.30($420) = $126 and $420 + $126 = $546.

or, 130% of $420 is 1.3($420) = $546.

notice that this is not the $600 original list price with which we started.

why doesn't this work?

the method does not work because 30% of $420 is not the same amount as the 30% of $600. it may seem obvious when stated this way, but it is a very common error made on problems of this type. we cannot just use the same percent and get back to the original amount because we are taking that percent of a different value.

to work problems of this type correctly, it is generally best to write an equation for the situation and then solve.

example: since (100% – 30%)(original price) = (sale price)

70% of the   (original price) is $420.

0.7x   = 420

equation image indicator

x = 600

the original cost was $600.

we may also solve this problem using the two-step method. working the problem in two steps requires us to use more algebra skills. we have to know that x = 1x (identity property of multiplicationtext annotation indicator) and that 1x – 0.3x = 0.7x (subtracting like terms). then we solve the problem as follows:

(original price) – 30%(original price) = sale price

x – 0.3x = 420

0.7x = $420

equation image indicator

x = 600

the original cost was $600.  

note that with both of the above methods we do obtain the correct original amount.

example: after a 5% pay raise, hermione is earning $22,680 per year. what was she earning before the pay raise?

105% of (original salary) = current salary

1.05x = 22,680

equation image indicator

x = 21,600

hermione earned $21,600 per year before the pay raise.

this is an example so maybe you will get how to at least do it!

since proposition states that a number is greater than 25, if is true then the number must actually be greater than 25.

this implies that all possible options, except 24, can be accepted