Our hypothesis is that female super models have a height greater

Solution

To find the p-value, we will use the t-test for a single sample because we are comparing the mean of a single sample (supermodels) to a known population mean (general female population), and the population standard deviation is unknown.

The formula for the t-score is:

t = (X̄ - μ) / (s/√n)

Where:

• X̄ is the sample mean
• μ is the population mean
• s is the sample standard deviation
• n is the sample size

Let's calculate the t-score first:

t = (69.6 - 62.3) / (2.4/√12)

After calculating the t-score, we will use a t-distribution table or a statistical software to find the p-value. The degrees of freedom (df) for a single sample t-test is n - 1.

Calculation

Let's plug in the values:

t = (69.6 - 62.3) / (2.4/√12) = 9.1

The degrees of freedom (df) is 12 - 1 = 11.

Now, we need to find the p-value associated with this t-score and df. Since we are testing for a height greater than the mean, it's a one-tailed test.

Unfortunately, I can't provide the exact p-value here as it requires a t-distribution table or statistical software. However, given the high t-score and low alpha level (0.01), it's highly likely that the p-value will be less than the alpha level, suggesting that we reject the null hypothesis and conclude that the mean height of supermodels is significantly greater than the mean height of the general female population.

Please use a t-distribution table or statistical software to find the exact p-value.