Final answer:
To determine if the supplement increased the mean mass of puppies, we can perform a one-sample t-test. The test statistic is calculated using the formula: t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size)). Comparing the calculated t-value to the critical t-value at the given significance level will give us the p-value and allow us to determine if the supplement had a significant effect.
Step-by-step explanation:
To determine whether the supplement has increased the mean mass of the puppies, we can perform a hypothesis test.
We can use a one-sample t-test since we have a sample size smaller than 30 and the population standard deviation is unknown.
The null hypothesis (H0) is that the mean mass of the puppies with the supplement is equal to the mean mass without the supplement. The alternative hypothesis (Ha) is that the mean mass of the puppies with the supplement is greater than the mean mass without the supplement. We can set a significance level of 0.01.
To calculate the test statistic, we can use the formula:
t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size))
Using the given data, the sample mean is 4.35 kg and the sample standard deviation is 0.0408 kg. The population mean is also 4.35 kg. Plugging these values into the formula, we get:
t = (4.35 - 4.35) / (0.0408 / sqrt(10))
t = 0 / (0.0408 / sqrt(10))
t = 0
With a t-value of 0, the p-value will be 1 (since the t-distribution is symmetric). Since the p-value is greater than the significance level of 0.01, we fail to reject the null hypothesis. Therefore, at the 0.01 level, we cannot conclude that the supplement has increased the mean mass of the puppies.
To estimate the p-value, we compare the calculated t-value to the critical t-value for the given significance level and degrees of freedom (df = sample size - 1). In this case, the t-value needed to reject the null hypothesis is not specified, so we cannot determine the p-value without that information.