Answers: Introduction to hypothesis testing
These are the answers to Questions: Introduction to hypothesis testing.
Please attempt the questions before reading these answers!
Q1
The following questions are on defining hypotheses.
1.1. Set the average number of pages (mean) to \(\mu\). Here, \(H_0: \mu=350\) and \(H_1: \mu<350\), and you would need a lower one-tailed test.
1.2. Set the percentage of defective products to be equal to \(D\). Here, \(H_0: D=0.1\) and \(H_1: D>0.1\), and you would need an upper one-tailed test.
1.3. Set \(\mu_a,\mu_b\) to be the average wait time in the two different branches. Here, \(H_0: \mu_a=\mu_b\) and \(H_1: \mu_a\neq\mu_b\), and you would need a two-tailed test.
1.4. Set \(\mu_x\) to be the average time of the express trains, and \(\mu_r\) to be the average time of the regular trains. Here, \(H_0: \mu_r=\mu_x\) and \(H_1: \mu_x>\mu_r\), and you would need a lower one-tailed test.
Q2
2.1. \(\alpha=0.15\)
2.2. \(\alpha=0.01\)
2.3. A paired t-test.
Q3
3.1. I reject \(H_0\) as the test statistic of \(3.12\) is greater than the critical value of \(2.58\). Therefore there is significant evidence to suggest the average daily sales of Boole Bars differ from 150.
3.2. I reject \(H_0\) as the test statistic of \(2.01\) is greater than the critical value of \(1.645\). Therefore there is significant evidence to suggest the proportion of customers who buy Lagrangian Lollipops exceeds \(40\%\).
3.3. I do not reject \(H_0\) as the test statistic of \(2.102\) is between the critical values of \(2.306\) and \(-2.306\). Therefore there is no significant evidence to suggest there is a difference in sweetness scores between the two recipes.
Version history and licensing
v1.0: initial version created 12/24 by Ellie Trace as part of a University of St Andrews VIP project.