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------------------------------------------------ Write the null and alternate hypotheses for the following scenario:

The mean weight of all 21-year-old women is 163 pounds. A random sample of 55 women athletes who are 21 years old showed a sample mean of 160 pounds with a standard deviation of 14 pounds. Researchers wanted to determine whether the mean weight for 21-year-old women athletes is significantly different from 163.

- Null Hypothesis ($H_0$): The mean weight of 21-year-old women athletes is equal to 163 pounds.
[tex] H_0: \mu = 163 \, \text{pounds} [/tex]

- Alternate Hypothesis ($H_a$): The mean weight of 21-year-old women athletes is not equal to 163 pounds.
[tex] H_a: \mu \neq 163 \, \text{pounds} [/tex]

The null hypothesis is that there is no significant difference between the mean weight for 21-year-old women athletes and 163 pounds. The alternative hypothesis is that there is a significant difference.

To write the null and alternative hypotheses, we need to first define the null hypothesis as the statement that there is no significant difference between the mean weight for 21-year-old women athletes and 163 pounds. The alternative hypothesis, on the other hand, would state that there is a significant difference.

So, in this case, the null hypothesis would be: H0: μ = 163 and the alternative hypothesis would be: H1: μ ≠ 163.

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