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Answer :
To express the null and alternative hypotheses for the given claim about the mean weight of female nurses working at a local hospital, we will follow these steps:
1. Understand the Claim:
- We are given that the mean weight of female nurses is equal to 128 lbs.
2. Define the Null Hypothesis (H₀):
- The null hypothesis represents the statement we assume to be true initially, or the claim that there is no effect or no difference from the given mean. In this scenario, the null hypothesis is that the mean weight of female nurses is 128 lbs.
- Symbolically, this can be written as:
[tex]\[
H₀: \mu = 128
\][/tex]
- Here, [tex]\( \mu \)[/tex] represents the mean weight of the population (female nurses).
3. Define the Alternative Hypothesis (H₁):
- The alternative hypothesis is what we consider if there is evidence against the null hypothesis. It reflects a possible difference or effect that we are looking to detect. In this case, since it's stated in the problem that the mean is equal to 128 lbs, the opposite would be that the mean weight is not 128 lbs.
- Symbolically, this is expressed as:
[tex]\[
H₁: \mu \neq 128
\][/tex]
In summary, the hypotheses for this claim are:
- Null Hypothesis (H₀): [tex]\( \mu = 128 \)[/tex]
- Alternative Hypothesis (H₁): [tex]\( \mu \neq 128 \)[/tex]
These hypotheses set up the framework for hypothesis testing, where we test if there's enough statistical evidence to reject the null hypothesis in favor of the alternative hypothesis.
1. Understand the Claim:
- We are given that the mean weight of female nurses is equal to 128 lbs.
2. Define the Null Hypothesis (H₀):
- The null hypothesis represents the statement we assume to be true initially, or the claim that there is no effect or no difference from the given mean. In this scenario, the null hypothesis is that the mean weight of female nurses is 128 lbs.
- Symbolically, this can be written as:
[tex]\[
H₀: \mu = 128
\][/tex]
- Here, [tex]\( \mu \)[/tex] represents the mean weight of the population (female nurses).
3. Define the Alternative Hypothesis (H₁):
- The alternative hypothesis is what we consider if there is evidence against the null hypothesis. It reflects a possible difference or effect that we are looking to detect. In this case, since it's stated in the problem that the mean is equal to 128 lbs, the opposite would be that the mean weight is not 128 lbs.
- Symbolically, this is expressed as:
[tex]\[
H₁: \mu \neq 128
\][/tex]
In summary, the hypotheses for this claim are:
- Null Hypothesis (H₀): [tex]\( \mu = 128 \)[/tex]
- Alternative Hypothesis (H₁): [tex]\( \mu \neq 128 \)[/tex]
These hypotheses set up the framework for hypothesis testing, where we test if there's enough statistical evidence to reject the null hypothesis in favor of the alternative hypothesis.
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