To determine the null and alternative hypotheses given the display, we need to identify what the given hypothesis test is evaluating. From the display, it can be determined that the test is assessing whether the population mean, denoted by [tex]\( \mu \)[/tex], is equal to a specific value.
Given the display, the null hypothesis ( [tex]\( H_0 \)[/tex] ) is the statement being tested, typically signifying no effect or no difference. The alternative hypothesis ( [tex]\( H_1 \)[/tex] ) signifies the statement we are trying to find evidence for, indicating an effect or difference.
### Step-by-Step Solution:
1. Identify the parameter being tested: The symbol [tex]\( \mu \)[/tex] (mu) represents the population mean.
2. Observe the test type: From the display, it states [tex]\( \mu \neq 5 \)[/tex]. This means the test is a two-tailed test checking for whether [tex]\( \mu \)[/tex] is not equal to 5.
3. Formulate the hypotheses:
- Null Hypothesis: The null hypothesis ( [tex]\( H_0 \)[/tex] ) will state that there is no difference, so [tex]\( \mu \)[/tex] is equal to a certain value.
- Alternative Hypothesis: The alternative hypothesis ( [tex]\( H_1 \)[/tex] ) suggests that there is a difference, so [tex]\( \mu \)[/tex] is not equal to that value.
Thus, using this information:
- The null hypothesis ( [tex]\( H_0 \)[/tex] ) is: [tex]\( \mu = 5 \)[/tex]
- The alternative hypothesis ( [tex]\( H_1 \)[/tex] ) is: [tex]\( \mu \neq 5 \)[/tex]
### Formatted Hypothesis:
- [tex]\( H_0: \mu = 5 \)[/tex]
- [tex]\( H_1: \mu \neq 5 \)[/tex]
### Filling in the Blanks:
[tex]\( H_0 \)[/tex] [tex]\( \square \quad \mu = 5 \)[/tex]
[tex]\( H_1 \)[/tex] [tex]\( \square \quad \mu \neq 5 \)[/tex]
Thus, the hypotheses are:
- [tex]\( H_0: \mu = 5 \)[/tex]
- [tex]\( H_1: \mu \neq 5 \)[/tex]
