Question

In the above hypothesis test in Q1, t-statistics test reject the null hypothesis, 40 is not within the confidence interval, but p value is smaller than the significance level alpha, how to explain this inconsistency?

a. Sample size is too large.

b. Sample size is too small.

c. Mistake in calculation when you do the hypothesis test

d. The dataset collected has low quality

Answer 1

A confidence interval is a range of values that is likely to contain an unknown population parameter. If we draw a random sample many times, a certain percentage of the confidence intervals will contain the population mean. This percentage is the confidence level.

P values measures how compatible our data are with the null hypothesis or measure the effect observed in our sample data if the null hypothesis is true.

So, if our significance level is 0.05, the corresponding confidence level is 95%. If the P value is less than our significance level 0.05, the hypothesis test is statistically significant. If the confidence interval does not contain the null hypothesis value i.e. 40, the results are statistically significant.

Hence the statement is not inconsistent. You can check this by taking large sample size. Because this statement perform well for large sample case.