Suppose you have observed a sample mean and you want to know how likely it is that you would observe these results by chance given nothing interesting was going on in the population regarding its mean.Which of the following would help you determine that?
A)Find the standard score corresponding to your sample mean and interpret it.
B)Find the percentage of time you would expect to see results at least this large, in the case where there is nothing interesting happening in the population.
C)Find the range of reasonable values for sample means of this size, given nothing interesting is going on in the population, and see if your sample mean is in that range or not.
D)All of the above.

Question

Quizplus · Accepted Answer

All the options provided are methods to determine how likely it is to observe a given sample mean by chance, assuming the population mean is not significantly different. Option A involves calculating the standard score (z-score) to see how many standard deviations away from the population mean the sample mean is. Option B involves calculating the p-value, which tells you the probability of observing a result as extreme as, or more extreme than, the sample mean under the null hypothesis. Option C involves constructing a confidence interval to see if the population mean could reasonably fall within a certain range around the sample mean. All these methods are used to infer whether the observed sample mean significantly differs from the population mean or if it could be due to random chance.

Suppose You Have Observed a Sample Mean and You Want