Question

Cicle true or false for each of the following statements:

a) The p-value tells us the probability the null hypothesis is true.

b) The sample mean of a random sample is not necessarily equal to the mean of the population.

c) Confidence Interval percentages tell us the probability that the population parameter we are solving for is within the limits of the calculated confidence interval.

d) If you gathered a sample and calculated the mean and standard deviation, all of the data points in your sample will be within one standard deviation of the mean.

e) Given a sufficiently large sample, the Central Limit Theorem allows us to make inferences on the mean of a population without knowing its distribution.

Answer 1

a) The p-value tells us the probability the null hypothesis is true.

True

The p-value is the likelihood of the observed data, given that the null hypothesis is true.

b) The sample mean of a random sample is not necessarily equal to the mean of the population.

True

As the sample may not necessarily represent the population, there is a possibility that some parameters may be underepresented or overepresented because ou selection of sample from population.

c) Confidence Interval percentages tell us the probability that the population parameter we are solving for is within the limits of the calculated confidence interval.

True

If repeated samples were taken and the 95% confidence interval was computed for each sample, 95% of the intervals would contain the population parameter. A 95% confidence interval has a 0.95 probability of containing the population parameter. 95% of the population distribution is contained in the confidence interval.

d) If you gathered a sample and calculated the mean and standard deviation, all of the data points in your sample will be within one standard deviation of the mean.

False

The data points can vary from one to any number of standard deviations from the mean.

e) Given a sufficiently large sample, the Central Limit Theorem allows us to make inferences on the mean of a population without knowing its distribution.

True

We can use the normal probability model to quantify uncertainty when making inferences about a population mean based on the sample mean provided we take sufficiently large random samples from the population.