Download Are you collecting a large enough sample?

Lesson Plan for AL Statistics (Teacher)
Title:
Pocket money
Level:
AL
Domain:
Sampling
Objective:
1.
2.
Taking survey on the amount of students’ pocket money per week.
To estimate the values of the parameters, pocket money, of the parent population,
students in Hong Kong.
Prerequisite Knowledge:
Normal distribution; Central Limit Theorem; Confidence Intervals & Gosset’s Student’s
t-distribution.
Motivation:
As reported from Ming Pao Daily News, student in Hong Kong has the largest amount of
pocket money as compared to all other area in South East Asia. Do you agree with it?
The survey in your class give another figure for the pocket money, what difference can
you tell us?
When the method of survey is changed, do the differences really tell another story?
There are essentially two reasons for the aims of sampling.
i.
To estimate the values of the parameters of the parent population;
ii.
To conduct a hypothesis test.
Points taking care for sampling:
Are the data relevant?
Are the data likely to be biased?
Does you method of collection distort the data?
Are you the right person to be collecting the data?
Are you collecting a large enough sample?
Is your sampling procedure appropriate in the circumstances?
AV Aids:
Street interview with teenagers on their consumer pattern and fashion favourites. Film
shots on commercial products for teenagers.
Main Task:
1.
2.
3.
4.
Random sample size of 5 students is chosen for taking the survey. And 100 samples
are recorded.
The distribution of their means is plotted. (Frequency against sample mean).
Measure the difference between the findings and the given amount, $151.
Using t-distribution to reorganize the problem.
Exercise:
The manufacturer of ABC cigarettes claims that his cigarettes have average nicotine
content of 18.3 milligrams. If a random sample of 8 ABC cigarettes has nicotine contents
of 20, 17, 21, 19, 22, 21, 20 and 16 milligrams, would you agree with the manufacturer’s
claim?
Discussions:
1.
2.
3.
Give different reasons why you might want to use a sample rather than to test every
member of the population for a survey.
What is the meaning of bias in sampling?
What makes for a good sample in survey?
Enrichment:
Hypothesis testing for the pocket money on the sample mean using the t-distribution is
x
performed. The test statistic is t 
with n-1 degrees of freedom.
̂ / n
Test for 2 tails and 1% significance level for the problem.
Task Sheet:
1.
The experiment is aimed to help you understand confidence intervals for estimate
the population mean from the sampling.
When a single die is thrown, probability for each outcome, 1 to 6, is 1/6.
Show that the expectation of the mean score is =3.5
And the standard deviation is =1.708
2.
Assumed that you know  but don’t know  and wish to construct a 90% confidence
interval for it.
Start by throwing a die once. Suppose a 4 is turned up. This sample size is one,
namely [4] and so the confidence interval is computed to be
4 – 1.645(1.708)/1
to
4 + 1.645(1.708)/1
i.e. 1.19
to
6.81
If the second throw gets a 6. Then the sample size is two, namely [4,6], and the other
confidence interval for the  is
Using =(4+6)/2=5
5 – 1.645(1.708)/2
to
5 + 1.645(1.708)/2
i.e. 3.01
to
6.99
This demonstrates that the larger the sample you take, the narrower the confidence
interval you get.
Organize different group to throw 5 dices for 100 times, out of these 100 confidence
intervals, how many do actually enclose the answer 3.5?