I have a question that involves explaining what is wrong in each of the following situations:

(a) A random sample of size 20 is taken from a population that is assumed to have a standard deviation of 12. The standard deviation of the sample mean is 12/20.

(b) A researcher tests the following null hypothesis: Ho:mean of the sample = 10

(c) A study with a sample mean = 48 reports statistical significance for Ha : u > 54.

(d) A researcher tests the hypothesis Ho : u = 50 and concludes that the population mean is equal to 50.

Help is appreciated I have answers already, but wanted to know if they were right. Thank you!!!!

It usually works the other way around; you give us your answer and we (the Jiskha volunteers) tell you whether you are right or not). We want to guide your thinking rather than do your homework for you.

Ummm, guiding our thinking doesn't work. I'm student teaching right now and I've been a student for year, sometimes you have to give the student the answer in order for them to figure out for themselves WHY it is right.

Sure! I'd be happy to help you evaluate your answers. Let's go through each situation and explain what is wrong if applicable:

(a) In this situation, the assumption is made that the standard deviation of the sample mean is equal to the population standard deviation divided by the sample size. However, this is incorrect. The correct formula for the standard deviation of the sample mean is the population standard deviation divided by the square root of the sample size. So, the correct calculation for the standard deviation of the sample mean in this case would be 12 / √20.

(b) In this situation, the researcher is testing a null hypothesis that states the mean of the sample is equal to 10. However, this is not sufficient information to evaluate what is wrong. We would need to know the alternative hypothesis and the significance level to determine if there is any issue with the study design or hypothesis testing.

(c) In this situation, the study claims statistical significance for the alternative hypothesis Ha: μ > 54, based on a mean of 48. However, this is incorrect. In hypothesis testing, statistical significance is determined by the p-value, which represents the probability of obtaining a sample mean as extreme as the one observed or more extreme, assuming the null hypothesis is true. Without further information, we cannot evaluate the study's claim of statistical significance.

(d) In this situation, the researcher tests the null hypothesis Ho: μ = 50 and concludes that the population mean is equal to 50. This is the correct conclusion to draw if the null hypothesis was adequately tested and the results support it. However, without more information, we cannot evaluate if there are any issues with the study design or hypothesis testing.

It is important to note that a thorough evaluation of the correctness of the answers requires more context and details. Nevertheless, based on the given information, hopefully, this explanation helps you assess your answers.