Answer :
The null hypothesis states that the mean weight of female dancers in the local modern dance company is equal to 141 lbs, while the alternative hypothesis suggests that the mean weight is not equal to 141 lbs.
The null and alternative hypotheses for the claim about the mean weight of female dancers in a local modern dance company can be expressed in symbolic form as follows:
Null hypothesis (H0): μ = 141 lbs
Alternative hypothesis (H1): μ ≠ 141 lbs
In this case, the null hypothesis states that the mean weight of female dancers in the local modern dance company is equal to 141 lbs. This means that if the null hypothesis is true, there is no significant difference between the mean weight and 141 lbs.
On the other hand, the alternative hypothesis suggests that the mean weight is not equal to 141 lbs. This means that if the alternative hypothesis is true, there is a significant difference between the mean weight and 141 lbs.
To clarify further, the null hypothesis is often used as a starting point in hypothesis testing. It represents the claim that there is no significant difference or effect. The alternative hypothesis, on the other hand, represents the claim that there is a significant difference or effect.
In this specific case, the alternative hypothesis is two-tailed because it includes the possibility that the mean weight could be both higher or lower than 141 lbs. The two-tailed alternative hypothesis is commonly used when we are interested in determining if there is a significant difference in either direction.
The null hypothesis states that the mean weight of female dancers in the local modern dance company is equal to 141 lbs, while the alternative hypothesis suggests that the mean weight is not equal to 141 lbs. These hypotheses form the basis for further statistical analysis to determine if there is a significant difference in the mean weight of the female dancers.
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