Apps. and Interpretation for IBDP Maths Ebook 1 | Page 359

4. The following table shows the ages of a certain number of interviewees participated in a
survey and X , the number of yogurt parfait cups they eat in a particular month:
Age
Number of yogurt parfait cups ate
1� X � 10 11� X � 20 21� X � 30 Total
18 or below 50 75 125 250
18 to 40 70 65 15 150
41 to 60 55 10 5 70
61 or above 25 4 1 a
Total 200 154 b n
(a)
For the number of yogurt parfait cups eaten, write down
(i) the class mark of the class 21� X � 30 ;
(ii) the upper class boundary of the class 1� X � 10 ;
(iii)
the modal class.
(b) (i) Write down the values of a , b and n .
[3]
(ii) Write down the exact value of the estimated mean of X .
(c)
A
(iii) Write down the estimated standard deviation of X .
[5]
An interviewee is selected at random. Find the probability that the interviewee is
at most 40 years old, given that the interviewee eats at least 11 yogurt parfait cups
in the month.
[3]
2
� test for independence is conducted at a 1% significance level.
(d) (i) Write down the null hypothesis of the test.
23
(e)
(f)
(g)
(h)
(ii) Write down the alternative hypothesis of the test.
Write down the degree of freedom of the test.
Find the p -value.
Write down the value of
�
2
calc
, the test statistic.
State the conclusion of the test with a reason.
[2]
[1]
[2]
[1]
[2]
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