University Statistics: Applied Statistical Methods, Module 5 Exam

This document presents solutions to an exam on applied statistical methods. The solutions address various concepts, including stating null hypotheses for different scenarios, such as those involving echinacea and colds, brain size and intelligence, and the ability of a psychic to predict coin flips. The document also covers the interpretation of p-values in relation to experimental results, the use of one-tailed tests, and the identification of Type I errors. Questions explore the significance of sample means, the relationship between alpha levels and the rejection of null hypotheses, and the importance of parameters versus sample statistics in hypothesis testing. The provided answers are supported by references to relevant statistical texts.

Running head: Applied Statistical Methods
Applied Statistical Methods
Name of the Student
Name of the University

2Applied Statistical Methods
Table of Contents
Q1...............................................................................................................................................3
Q2...............................................................................................................................................3
Q3...............................................................................................................................................3
Q4...............................................................................................................................................3
Q5...............................................................................................................................................4
Q6...............................................................................................................................................4
Q7...............................................................................................................................................4
Q8...............................................................................................................................................4
Q9...............................................................................................................................................5
Q10.............................................................................................................................................5
References:.................................................................................................................................6

3Applied Statistical Methods
Q1.
a)
Null Hypothesis: Echinacea does not decreases the length of colds.
b)
Null Hypothesis: There is no linear relation between brain size and intelligence.
c)
Null Hypothesis: The psychic can predict the outcome of a coin flip.
d)
Null Hypothesis: Pain relief remains unchanged with the drug.
Q2.
The mean with M = 60 is one standard deviation away from μ=50.As 68 % of the area lies
within one standard deviation.
Q3.
The experimenter’s confidence in the theory should decrease as the p value is higher than the
standard 0.05.
Q4.
No the researcher cannot claim that the exercise has no effect a there might be interaction
between exercise group and the diet control.

4Applied Statistical Methods
Q5.
A one tailed test is used when the critical area of distribution falls on one side of the mean.
A one tailed test has more statistical power than a two tailed test at the same level of
significance.
Testing the hypothesis that sample mean is higher than a given value would normally be done
using a one tailed test.
Q6.
The significance value is the value that the probability values have to be measured against.
Probability value is the chance of getting the sample statistic by chance alone given the null
hypothesis is true.
Q7.
The mean score of the experimental group was higher than the mean score of the control
group.
Q8.
Type 1 error means rejecting the null hypothesis even though it is true.
Probability that you will make a Type I error given that the null hypothesis is true = 0.01
Probability that you will make a Type I error given that the null hypothesis is false = 0

5Applied Statistical Methods
Q9.
Testing the hypothesis that the sample mean is 42 does not make sense because hypothesis
testing are about parameters and not sample statistics.
Q10.
True/false: It is easier to reject the null hypothesis if the researcher uses a smaller alpha (α)
level.
False.

6Applied Statistical Methods
References:
Triola, M.F., Goodman, W.M., Law, R. and Labute, G., 2014. Elementary statistics. Reading,
MA: Pearson/Addison-Wesley.
Cooke, D. and Clarke, G.M., 2016. A basic course in statistics. Arnold.