Question

In an experiment to assess the strength of the hunger drive in rats, 30 previously trained animals were deprived of food for 24 hours. At the end of the 24 -hour period, each animal was put into a cage where food was dispensed if the animal pressed a lever. The length of time the animal continued pressing the bar (although receiving no food) was recorded for each animal. If the data yielded a sample mean of 19.3 minutes with a standard deviation of 5.2 minutes, estimate the true mean time and calculate the margin of error.

Short answer

Answer: The estimated true mean time is between 17.36 minutes and 21.24 minutes.

Step-by-step solution

1. Calculate the estimated standard error

We can calculate the estimated standard error by dividing the standard deviation by the square root of the sample size: Estimated Standard Error = \(\frac{Standard Deviation}{\sqrt{Sample Size}}\) Estimated Standard Error = \(\frac{5.2}{\sqrt{30}}\) = \(0.95\) minutes.

2. Determine the degrees of freedom

The degrees of freedom in this case would be the sample size minus 1: Degrees of Freedom = \(Sample Size - 1\) Degrees of Freedom = \(30 - 1 = 29\).

3. Find the critical T-score

We will use a 95% confidence interval, which means we are looking for the T-score that corresponds to the center 95% of the T-distribution. The T-score depends on the degrees of freedom, in this case, 29. Using a T-distribution table or calculator, we find the critical T-score: T-score = \(2.045\).

4. Calculate the margin of error

Now, we will calculate the margin of error by multiplying the critical T-score by the estimated standard error: Margin of Error = \(Critical T-score × Estimated Standard Error\) Margin of Error = \(2.045 × 0.95\) = \(1.94\) minutes.

5. Estimate the true mean time

Finally, we will use the sample mean and the margin of error to estimate the true mean time: Lower Bound = Sample Mean - Margin of Error = \(19.3 - 1.94\) = \(17.36\) minutes. Upper Bound = Sample Mean + Margin of Error = \(19.3 + 1.94\) = \(21.24\) minutes. We can estimate that the true mean time that the rats will continue pressing the lever is between \(17.36\) minutes and \(21.24\) minutes with a 95% confidence interval.