Which of the following statements is correct?Question 5Select one:a.A p-value estimates the probability that the observed difference between two groups might have occurred due to chance alone.b.A p-value estimates the probability that the observed difference between two groups might have occurred due to one group being better than the other.c.A confidence interval cannot provide information about the precision of a study result.d.A confidence interval can estimate the sample size of the study.

Which of the following statements is NOT true regarding p-value? The result of every hypothesis test includes a p-value The p-value is the true test of significance The p-value represents the probability that the null hypothesis is TRUE If the p-value is less than or equal to 0.05, there is NOT a significant difference -- fail to reject the Null hypothesis

Regarding point estimates and confidence interval estimates, which one of the following statements is FALSE?Group of answer choicesFor both estimates we assume that the observations are independent.For both estimates we assume that the population distribution of the variable (X) is approximately Normal.An indication of the error due to sampling is only provided for a confidence interval estimate.For both estimates, a larger sample size means a more precise estimateBoth estimates are calculated using sample data

Suppose (35,40) is a 95% confidence interval estimate for a population mean 𝜇. Which of the following are true statements?I. There is a .95 probability that 𝜇 is between 35 and 40.II. If 100 random samples of the given size are picked and a 95% confidence interval is calculated from each, then 𝜇 will be in 95 of the resulting intervals.III. If 95% confidence intervals are calculated from all possible samples of the given size, 𝜇 will be in 95% of these intervals.I and III and IIIII and IIII, II, and IIINone of the above gives the complete set of true responses.

A student was asked to find a 95% confidence interval for the proportion of students who take notes using data from a random sample of size n = 89. Which of the following is a correct interpretation of the interval 0.1 < p < 0.2?Check all that are correct.There is a 95% chance that the proportion of notetakers in a sample of 89 students will be between 0.1 and 0.2.There is a 95% chance that the proportion of the population is between 0.1 and 0.2.With 95% confidence, the proportion of all students who take notes is between 0.1 and 0.2.With 95% confidence, a randomly selected student takes notes in a proportion of their classes that is between 0.1 and 0.2.The proprtion of all students who take notes is between 0.1 and 0.2, 95% of the time.

Explain how interpreting the confidence interval from your hypothesis test could help you make a better decision than just interpreting the p-value. Write two or three sentences.