I hope you are doing well.
I have been successfully solving hypothesis problems when I am given the percentage on the claim. However, now I have to solve problems with no given percentage. Have a look at these 2 examples.
Example 1: the candy maker recently claimed that M&M’s were so much fun because they were a perfect rainbow, that is, each bag they made contained equal numbers of each of the five colors. The bag came with:
Brown: 19 Blue: 5 Green: 5 Orange: 9 Yellow: 10
Example 2: Dr. Joseph claims that very young children are equally attracted to different colored balls. There are three balls to choose from, all identical in size.
How do I formulate the null hypothesis?
Thank you for your time.
There are 48 M&M's in the bag and 5 colors, so one possible null hypothesis is that there are 9 Brown, 9 Blue, 9 Green, 9 Orange, and 9 Yellow in a typical bag. Or you could say the null hypothesis is that there are 10 Brown, Blue, Green, Orange, and Yellow M&M's in a bag. In terms of percentages, each color appears in 20% of the total M&M's in the bag is the null hypothesis. The alternative hypothesis is the actual percentage of M&M colors differs from a perfect 20%-20%-20%-20%-20% split.
For the children and balls, one null hypothesis could be that the proportion of children who pick color 1 is 1/3, color 2 is 1/3, and color 3 is 1/3. The alternative is that the population proportions differ from this.