For each of the following samples that were given an experimental treatment, test whether these samples represent populations that are different from the general population: (a) a sample of 10 with a mean of 44, (b) a sample of 1 with a mean of 48. The general population of individuals has a mean of 40, a standard deviation of 6, and follows a normal curve. For each sample, carry out a Z test using the five steps hypothesis testing with a two-tailed test at the .05 significance level, and make a drawing of the distributions involved.

To test whether the given samples represent populations that are different from the general population, we can perform a Z-test. A Z-test compares a sample mean to a population mean, taking into account the sample size, population standard deviation, and significance level.

Step 1: State the null and alternative hypotheses:
- Null hypothesis (H0): The sample mean is equal to the population mean.
- Alternative hypothesis (Ha): The sample mean is different from the population mean.

Step 2: Determine the significance level:
The given significance level is 0.05, meaning we have a 5% chance of rejecting the null hypothesis when it is true (Type I error).

Step 3: Calculate the test statistic:
For each sample, we need to calculate the Z-score using the formula: Z = (x - μ) / (σ / sqrt(n)), where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

For sample (a):
- Sample mean (x): 44
- Population mean (μ): 40
- Population standard deviation (σ): 6
- Sample size (n): 10

Z = (44 - 40) / (6 / sqrt(10)) = 2.108

For sample (b):
- Sample mean (x): 48
- Population mean (μ): 40
- Population standard deviation (σ): 6
- Sample size (n): 1

Z = (48 - 40) / (6 / sqrt(1)) = 8 / 6 = 1.333

Step 4: Determine the critical value:
Since we are using a two-tailed test, we need to find the critical Z-values that correspond to a significance level of 0.025 on each side of the distribution. We can use a Z-table or statistical software to find the critical values. For a significance level of 0.05, the critical Z-value is approximately ±1.96.

Step 5: Compare the test statistic with the critical value and make a decision:
If the calculated Z-value is greater than the critical value of ±1.96, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

For sample (a):
|2.108| > 1.96, so we reject the null hypothesis. The sample represents a population that is different from the general population.

For sample (b):
|1.333| < 1.96, so we fail to reject the null hypothesis. The sample does not represent a population that is different from the general population.

To illustrate the distributions involved, you can create two normal distribution curves, one representing the general population with a mean of 40 and a standard deviation of 6, and the other representing each sample with their respective means. The Z-test involves comparing the sample mean to the population mean and evaluating if it lies within the critical region or not.