Download Worksheet for AL Statistics (Student)

Worksheet for AL Statistics (Student)
Title: Chocolate Dispenser
Level: Key Stage – Advanced
Domain: Tests of Hypotheses
Objectives:
1. Build up the statistical hypotheses for Type I and Type II Errors.
2. Computing the numerical values for Type I (α) and Type II (β) Errors.
3. Solving tests concerning population mean μ.
4.
Solving tests concerning proportion p.
Prerequisite Knowledge:
1. Normal distribution
2. Sampling distribution
3. Estimation of parametersμ & p
Problem:
1. The soft-drink dispenser can never give exact volume each time. Why?
2. How to adjust the dispensed volume for the constant volume of the cup?
Motivation:
1. Chocolate dispenser at Mc Donald’s is an
automate machine.
2. The soft-drink machine is regulated so that
the amount of hot chocolate dispensed 210
ml per cup in average.
3. Collect readings for the volume mentioned.
Main Task
1. Try to collect one cup of hot chocolate for each student.
2. Ask students to suggest a good method for measuring the contents of each cup, provided
they can drink the chocolate later.
3. Collect the counts for the data.
4. Compute the sample parameters by hands.
5. Figure out the related graphs.
6. Plot the graphs by software provided.
7. Visualize the related speculation for the population.
8. Try to experience the simulation program of sampling distribution.
Exercise:
1.
A random sample of size 20 from a normal distribution has a mean of 32.8 and a
standard deviation 4.51. Does this suggest, at the 0.05 level of significance, that the
population mean is greater than 30?
2.
A random sample of 200 voters in the city are asked if they favor a new 5% sales tax. If
more than 110 but less than 130 favor the sales tax, we shall conclude that 60% of the
voters are for it.
a.
b.
Find the probability of committing a type I error if 60% of the voters favor the tax.
What is the probability of committing a type II error using this procedure if actually
only 48% of the voters are in favor of the new sales tax?
Enrichment:
Organize a survey for the whole form. Taking the statistic of one class and estimate the type I
and type II errors for the whole population of the form.
Task Sheet for Class Discussion
1. How to measure the contents of chocolate drinks, provided the chocolate is still drinkable.
2. What are the differences for the statements, ‘accept a hypothesis’ and ‘no evidence to
reject’?
3. Sketch the distribution for the hypotheses, and shades the corresponding area for Type I
and Type II error. How are they related to each other when one of them is changing?
4. Can we control the Type I error by the size of the critical region?
5. What will happen when the sample size is increased?