The average height of 18-year-old American women is 64.2 inches. You wonder whether the mean height of this year’s female graduates from your local high school is different from the national average. You measure an SRS of 78 female graduates and find that = 63.1 inches. What are your null and alternative hypotheses?

The null hypothesis (H₀) states that the mean height of this year's female graduates from the local high school is equal to the national average, which is 64.2 inches.

The alternative hypothesis (H₁) states that the mean height of this year's female graduates from the local high school is different from the national average.

To determine the null and alternative hypotheses, we need to consider the research question and the information provided.

The research question is whether the mean height of this year's female graduates from your local high school is different from the national average.

The null hypothesis (H0) is a statement of no difference or no effect. In this case, the null hypothesis would be that the mean height of this year's female graduates from your local high school is equal to the national average.

The alternative hypothesis (Ha) is a statement that contradicts or negates the null hypothesis. In this case, the alternative hypothesis would be that the mean height of this year's female graduates from your local high school is different from the national average.

Therefore, the null hypothesis (H0) would be: The mean height of this year's female graduates from your local high school is equal to the national average.

The alternative hypothesis (Ha) would be: The mean height of this year's female graduates from your local high school is different from the national average.

In symbolic notation:
H0: μ = 64.2 inches
Ha: μ ≠ 64.2 inches

Where μ represents the population mean height of the female graduates.

Ha: mean1 = mean2

Ho: mean1 ≠ mean2 (before sample measured)

or

Ho: mean1 > mean2 (after sample measured)