We want to analyze the growth of rabbits on a farm. For this, 13 rabbits are chosen and measured, obtaining an average size of the sample of 5.3 centimeters and a sample variance of 19.3. For his part, a veterinarian dedicated to research states that the average size of rabbits in the population is greater than 4.5 centimeters. Verify this statement by applying a hypothesis test with a significance level of 0.01. YOU MUST CARRY OUT THE 5 RESPECTIVE STEPS OF A HYPOTHESIS TEST AND THE RESPECTIVE GRAPH WITH THE CORRESPONDING DATA Evaluate the P value

To evaluate the P value, we can use the t-distribution since the sample size is relatively small (n = 13) and the population standard deviation is unknown.

Step 1: State the null and alternative hypotheses:
Null hypothesis (H0): The average size of rabbits in the population is less than or equal to 4.5 centimeters.
Alternative hypothesis (Ha): The average size of rabbits in the population is greater than 4.5 centimeters.

Step 2: Select the appropriate test statistic:
Since we don't know the population standard deviation, we will use the t-test statistic. The test statistic is calculated as:
t = \frac{\bar{x} - \mu}{s/\sqrt{n}}
where \bar{x} is the sample mean, \mu is the population mean, s is the sample standard deviation, and n is the sample size.

Step 3: Set the significance level:
The significance level is given as 0.01.

Step 4: Calculate the P value:
To calculate the P value, we need to find the t-distribution with n-1 degrees of freedom (df = 13-1 = 12) and the t-score corresponding to the sample mean.

Using the t-distribution table or a statistical calculator, we find that the critical t-value for a one-tailed test with df = 12 and a significance level of 0.01 is approximately 2.681.

Next, we calculate the t-score:
t = \frac{5.3 - 4.5}{\sqrt{\frac{19.3}{13}}} \approx 1.21

Finally, we find the P value using the t-distribution:
P value = P(T > 1.21) = 1 - P(T <= 1.21)

Step 5: Compare the P value with the significance level:
If the P value is less than the significance level (0.01), we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

Answer:
To evaluate the P value, we calculated a t-score of approximately 1.21. Using the t-distribution with df = 12, we found that the P value is greater than 0.01. Therefore, we fail to reject the null hypothesis.

In conclusion, there is not enough evidence to support the claim that the average size of rabbits in the population is greater than 4.5 centimeters, based on the given sample.