| Exam Board | OCR MEI |
|---|---|
| Module | Further Statistics Major (Further Statistics Major) |
| Session | Specimen |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Chi-squared goodness of fit |
| Type | Spreadsheet-based chi-squared test |
| Difficulty | Standard +0.3 This is a straightforward chi-squared test of independence with standard spreadsheet interpretation. Students must identify the test, state hypotheses, calculate missing expected frequencies and contributions using given formulas, and complete the test using tables. All steps are routine applications of the chi-squared procedure taught in Further Statistics, requiring no novel insight or complex reasoning. |
| Spec | 5.06a Chi-squared: contingency tables |
| A | B | C | D | E | F | |
| 1 | Source | Age group | ||||
| 2 | of news | 18-32 | 33-47 | 48-64 | 65+ | |
| 3 | T | 63 | 61 | 71 | 80 | 275 |
| 4 | I | 33 | 33 | 22 | 12 | 100 |
| 5 | N | 9 | 8 | 11 | 20 | 48 |
| 6 | R | 4 | 9 | 9 | 5 | 27 |
| 7 | 109 | 111 | 113 | 117 | 450 | |
| 8 | ||||||
| 9 | Expected frequencies | |||||
| 10 | 66.61 | 67.83 | 69.06 | 71.50 | ||
| 11 | 24.22 | 24.67 | 26.00 | |||
| 12 | 11.63 | 11.84 | 12.05 | 12.48 | ||
| 13 | 6.54 | 6.66 | 6.78 | 7.02 | ||
| 14 | ||||||
| 15 | Contributions to the test statistic | |||||
| 16 | 0.20 | 0.69 | 0.05 | 1.01 | ||
| 17 | 3.18 | 2.82 | 7.54 | |||
| 18 | 0.59 | 0.09 | 4.53 | |||
| 19 | 0.99 | 0.82 | 0.73 | 0.58 | ||
| 20 | test statistic | 25.45 | ||||
| Answer | Marks | Guidance |
|---|---|---|
| 9 | (i) | (A) |
| [1] | 2.2a | |
| 9 | (i) | (B) |
| [1] | 1.2 | |
| 9 | (i) | (C) |
| Answer | Marks | Guidance |
|---|---|---|
| source | B1 | |
| [1] | 2.5 | N |
| 9 | (ii) | 113 |
| Answer | Marks |
|---|---|
| 25.11 | M1 |
| Answer | Marks |
|---|---|
| [4] | 3.4 |
| Answer | Marks |
|---|---|
| C1.1 | E |
| Answer | Marks | Guidance |
|---|---|---|
| 9 | (iii) | P |
| Answer | Marks |
|---|---|
| primary news source | B1 |
| Answer | Marks |
|---|---|
| [4] | 3.3 |
| Answer | Marks | Guidance |
|---|---|---|
| 9 | (iv) | For age group 18-32 and 33-47, the |
| Answer | Marks |
|---|---|
| that primary sources are as expected | E1 |
| Answer | Marks |
|---|---|
| [3] | 3.5a |
| Answer | Marks |
|---|---|
| 3.5a | N |
Question 9:
9 | (i) | (A) | Sample size = 450 | B1
[1] | 2.2a
9 | (i) | (B) | Chi-squared test [for a contingency table] | B1
[1] | 1.2
9 | (i) | (C) | H : no association between age and news
0
source
H : some association between age and news
1
source | B1
[1] | 2.5 | N
9 | (ii) | 113
D11= (cid:117)100
450
=25.11
(cid:11)8(cid:16)11.84(cid:12)2
C18 = (cid:32)1.25
11.84
(cid:11)22(cid:16)25.11(cid:12)2
D17 = (cid:32)0.39
25.11 | M1
A1
M1
A1
E
[4] | 3.4
1.1
I1.1
C1.1 | E
M
(cid:11)O(cid:16)E(cid:12)2
M1 for applied at
E
least once
A1 for both correct: accept
1.245, 0.385
(NB one can be calculated by
subtraction)
9 | (iii) | P
Degrees of freedom = 9
S
Critical value = 16.92
Test statistic = 25.45
25.45 > 16.92 so reject H
0
There is sufficient evidence to suggest that
there is some association between age and
primary news source | B1
B1
M1
A1
[4] | 3.3
1.1
2.2b
3.5a
9 | (iv) | For age group 18-32 and 33-47, the
contributions of 3.18 and 2.82 show that
more than expected have primary source the
internet
For age group 65+, the contributions of 7.54
and 4.53 show that fewer than expected have
primary source the internet and more than
expected have primary source newspapers.
For age group 48 - 64 the contributions show
that primary sources are as expected | E1
E1
E1
[3] | 3.5a
3.5a
3.5a | N
E
Allow other suitable answers.
M
Max 2 out of 3 if numerical
values of contributions to test
statistic not mentioned9 A random sample of adults in the UK were asked to state their primary source of news: television (T), internet (I), newspapers (N) or radio (R). The responses were classified by age group, and an analysis was carried out to see if there is any association between age group and primary source of news.
Fig. 9 is a screenshot showing part of the spreadsheet used to analyse the data. Some values in the spreadsheet have been deliberately omitted.
\begin{table}[h]
\begin{center}
\begin{tabular}{|l|l|l|l|l|l|l|}
\hline
& A & B & C & D & E & F \\
\hline
1 & Source & \multicolumn{4}{|c|}{Age group} & \\
\hline
2 & of news & 18-32 & 33-47 & 48-64 & 65+ & \\
\hline
3 & T & 63 & 61 & 71 & 80 & 275 \\
\hline
4 & I & 33 & 33 & 22 & 12 & 100 \\
\hline
5 & N & 9 & 8 & 11 & 20 & 48 \\
\hline
6 & R & 4 & 9 & 9 & 5 & 27 \\
\hline
7 & & 109 & 111 & 113 & 117 & 450 \\
\hline
8 & & & & & & \\
\hline
9 & & \multicolumn{4}{|l|}{Expected frequencies} & \\
\hline
10 & & 66.61 & 67.83 & 69.06 & 71.50 & \\
\hline
11 & & 24.22 & 24.67 & & 26.00 & \\
\hline
12 & & 11.63 & 11.84 & 12.05 & 12.48 & \\
\hline
13 & & 6.54 & 6.66 & 6.78 & 7.02 & \\
\hline
14 & & & & & & \\
\hline
15 & \multicolumn{5}{|c|}{Contributions to the test statistic} & \\
\hline
16 & & 0.20 & 0.69 & 0.05 & 1.01 & \\
\hline
17 & & 3.18 & 2.82 & & 7.54 & \\
\hline
18 & & 0.59 & & 0.09 & 4.53 & \\
\hline
19 & & 0.99 & 0.82 & 0.73 & 0.58 & \\
\hline
20 & \multicolumn{5}{|r|}{test statistic} & 25.45 \\
\hline
\end{tabular}
\captionsetup{labelformat=empty}
\caption{Fig. 9}
\end{center}
\end{table}
\begin{enumerate}[label=(\roman*)]
\item (A) State the sample size.\\
(B) Give the name of the appropriate hypothesis test.\\
(C) State the null and alternative hypotheses.
\item Showing your calculations, find the missing values in cells
\begin{itemize}
\item D11,
\item D17 and
\item C18.
\item Complete the appropriate hypothesis test at the $5 \%$ level of significance.
\item Discuss briefly what the data suggest about primary source of news. You should make a comment for each age group.
\end{itemize}
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Statistics Major Q9 [13]}}