10. A random sample of n=36 scores is selected from a normal distribution with a mean of u=60. After a treatment is administered to the individuals in the sample, the sample mean is found to be M=52.

What is your question? you need to have some measure of variability.

To analyze this data, we can use the concept of hypothesis testing. Hypothesis testing allows us to make inferences about a population based on a sample of data.

In this case, we want to determine if the treatment had a significant effect on the sample mean score. To do this, we can set up a null hypothesis (H0) and an alternative hypothesis (H1) based on what we want to test.

H0 (Null Hypothesis): The treatment had no effect, and the population mean is still u=60.
H1 (Alternative Hypothesis): The treatment had an effect, and the population mean is not u=60.

To test these hypotheses, we can use a t-test because the population standard deviation is unknown. Since the sample size is larger than 30, we can assume that the distribution of sample means will be approximately normally distributed.

To perform the t-test, we need to calculate the t-statistic and compare it to the critical t-value at an appropriate significance level. The t-statistic is calculated using the formula:

t = (M - u) / (s / sqrt(n))

Where M is the sample mean, u is the assumed population mean under the null hypothesis, s is the sample standard deviation, and n is the sample size.

In our case, M=52, u=60, and n=36. However, we don't have the sample standard deviation (s) explicitly mentioned. We would need that information to calculate the t-statistic accurately.

Once we have the t-statistic, we can compare it to the critical t-value from a t-distribution table or use statistical software to determine the p-value associated with that t-value. The p-value is the probability of observing a sample mean as extreme as our observed sample mean (52) if the null hypothesis (H0) is true. If the p-value is below the chosen significance level (e.g., 0.05), we reject the null hypothesis.

It is important to note that conducting hypothesis tests requires additional data beyond what you provided to obtain conclusive results.