MA0212 Assignment 8 Mark ___/ 35
1.
State the Null Hypothesis, the Alternative hypothesis, and the Claim for the
following in terms of parameter(s):
For
example: The mean age of
teddy bears brought to college is 15.9 years. The average age of teddy
bears in Ontario is 21.5 years, with a standard deviation of 3.8 years. The
authors of the teddy bear study claim that teddy bears brought to college are
the same age as the ones left at home.
The answer should look like the following:
H0: 
H1:
Claim: H0 is true.
a) The mean of a sample of the age of
students in grade 12 in a certain community was 16.5 years. The average age of students in Ontario in
grade 12 was 17.3 years and the standard deviation was 0.7. The authors of the study say that in this
community Grade 12 students are younger than the Ontario average.
b) A study of the number of incidences
of a certain disease in a community was 12.14 per thousand. The provincial
average was 12.87 per thousand. The authors contended that there was no
difference in the rates. [ 6
marks]
2. State whether the following are Type 1 or
Type 2 errors:
a) A study of dental cavities in
children showed that there was no effect in using a certain toothpaste, when in
truth, there was an effect.
b) A study of regular long term use of
antiseptic soap in the home showed that there was a positive effect on
infections in children, when in fact, there was a no effect.
[
2 marks]
3.
Fill in the blanks. “ If the chance of a Type 1 error is reduced by _______________(increasing/decreasing
) the confidence level, the chance of a Type 2 error is
____________(increased/decreased). [
2 marks]
4. Find the critical values(s) for the following:
a) z score, 0.20 level of significance,
right tailed test
b) z score , 0.01 level of
significance, two tailed
c) t score, 
, df = 11, left tailed
d) chi square, df = 12, 0.05 level of significance, right tailed [ 5 marks]
5.
State the test statistic: (include type (t, z, chi-square etc.) and value)
a)
b) 
c) 
d) 
e)
[10
marks]
6.
A
hospital statistician records a sample (size = 24) of the wait times for a
particular operation. It is found that the sample mean wait time is 7.36 weeks,
with a standard deviation of 2.04 weeks. The statistician claims that this is
no different from the provincial mean wait time of 5.45 weeks at a 0.10 level
of significance.
Using the Traditional Method, show
whether the statistician’s claim is upheld or not. [ Marks will be given for stating the
hypotheses in terms of values, the claim in terms of the hypothesis,
calculation of the correct test statistic, finding the critical point(s),
accepting or rejecting the hypotheses in terms of your critical area, and the
summary.] [
10 marks]
Use
the following as a Template:
Null
Hypothesis:
Alternative
Hypothesis:
Claim:
Level
of Significance: alpha=
Critical
Value(s) : State
Table used:
Test
Statistic Formula:
Calculation:
State
whether you accept of reject the Null Hypothesis:
State
whether you accept or reject the Alternate Hypothesis:
State
whether the Claim is upheld:
Total [ 35 marks]
