Oth- Caution: Give explanations for your answers, even for the True-False questi

Question

Oth- Caution: Give explanations for your answers, even for the True-False questions erwise you will not receive credit. 1. (16 pts) True or false: (a) You get a p-value of 0.25. There is a 75% chance that the alternative hypothesis is true. (b) If you increase the sample size, you have a better chance of rejecting a null hypothesis that is false (when all else about the population remains unchanged). (c) Your research colleague calculates by hand a value of the correlation of 1.14. He says this shows that there is a strong, positive linear association between the two variables. (d) When data are randomly sampled from the same population, a 95% confidence interval constructed from a sample of 100 units should be narrower than a 95% confidence interval constructed from a sample of 200 units.

Explanation / Answer

a) p - value is the probability of getting the given sample results given that the null hypothesis was true. It has nothing to do with the alternate hypothesis here. Therefore the given statement here is FALSE

b) If we increase the sample size, we get better results from both sides. This means that given the null hypothesis is false, the probability to reject the null hypothesis increases and also given the null hypothesis to be true, the probability of retaining the null hypothesis also increases. Therefore the given statement here is TRUE

c) The correlation coefficient ranges from -1 to +1, it cannot be more than 1. Therefore the given statement here is FALSE

d) As the sample size increases, the margin of error decreases and therefore the confidence interval becomes narrower. Therefore the confidence interval with n = 100 would be wider than the sample size of n = 200. Therefore the given statement here is FALSE

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