A cereal manufacturer claims that there are an average of 200 raisins in each box of cereal. Let $$ \mu $$ represent the average number of raisins per box of cereal. You want to test this claim. What is the null hypothesis, $$ H_{0} $$, for this situation? $$ \mu200 $$ $$ \quad $$ Dosse

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A cereal manufacturer claims that there are an average of 200 raisins in each box of cereal. Let $$ \mu $$ represent the average number of raisins per box of cereal. You want to test this claim. What is the null hypothesis, $$ H_{0} $$, for this situation? $$ \mu<200 $$ $$ \mu \leq 200 $$ $$ \mu>200 $$ $$ \quad $$ Dosse

UpStudy AI · Accepted Answer

In hypothesis testing, the null hypothesis ($$ H_0 $$) represents a statement of no effect or no difference, and it is what we seek to test against. In this case, the manufacturer claims that the average number of raisins in each box of cereal is 200.

The null hypothesis should reflect this claim. Therefore, the appropriate null hypothesis for this situation is:

$$
H_0: \mu = 200
$$

However, since the options provided do not include $$ H_0: \mu = 200 $$, we need to consider the closest option that represents the null hypothesis correctly.

The options given are:
- $$ \mu < 200 $$
- $$ \mu \leq 200 $$
- $$ \mu > 200 $$

Among these, the option $$ \mu \leq 200 $$ is the most appropriate because it includes the possibility that the average number of raisins could be equal to 200, which aligns with the manufacturer's claim.

Thus, the correct null hypothesis is:

$$
H_0: \mu \leq 200
$$
The null hypothesis is $$ \mu \leq 200 $$.

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