Question

Skittles is a brand of fruit-flavored candy, currently produced and marketed by the Wrigley Company, a division of Mars, Inc. Skittles consist of hard sugar shells imprinted with the letter "S". They come in five different colors: Red, Purple, Green, Orange, and Yellow. They claim that there are an equal number of Skittles distributed for each color into their packages. You are interested if Skittles are including more Orange Skittles into their packages than the rest. Out of the 200 Skittles you counted, 43 of them were Orange. For this study, you will use a significance level of 0.05.

Please answer the following questions below.
Using the context above, what is the probability of making a Type 1 error? 0 43/200 0.05 05
Not enough information given
a) Have a new observed statistic of 86/400:
1. Power will increase
2. Power will decrease
3. Power will remain the same
b) Change your significance level from 0.05 to 0.10:
1. Power will increase
2. Power will decrease
3. Power will remain the same

Answer 1

0.05

a) Power will remain the same

b) Power will increase

Explanation:

Total number of Skittles = 200

Number of orange Skittles = 43

Level of Significance = 0.05

Probability of making a type 1 error is the probability of rejecting the null hypothesis when it is true. The probability of making a type 1 error is the significance level

Therefore type 1 error = 0.05

a) If the observed statistic is 86/100, the power will increase.

The power is the probability of rejecting the null hypothesis when it is false. (i.e not making a type 2 error)

The power depends on sample size, significance level, variability in the response variable, etc.

Since 43/200 is the same as 86/400 in value and the significance level is not said to be changed, the power will remain the same.

b) Power depends on significance level. Therefore, if the significance level is changed from 0.05 to 0.10, the power will increase.