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To evaluate it, she splits...

A year 5 teacher is interested in a new method of testing fractions. To evaluate it, she splits the year group randomly into two groups, with 16 to be taught using the new method, and 15 to be taught by the old method. Score on an end of term test of the material were as follows

Old Method New Method

11 13

14 16

21 25

26 33

25 31

22 29

15 20

26 33

22 27

20 25

31 38

32 23

15 30

25 29

23 24

19

a) Histograms for the two data sets are presented below. Comment on whether it seems justified to assume scores are from normal distributions with equal standard deviations.

Old Method Bin Frequency

Bins 14 2

14 19 3

19 24 5

24 29 4

29 34 2

34 More 0

New Method Bin Frequency

14 14 1

19 19 1

24 24 3

29 29 5

34 34 4

39 More 1

b) Summary statistics for the two data sets are as follows

Mean Standard n

Deviation

Old Method 21.69 5.93 15

New Method 26.40 6.65 16

The teacher wishes to investigate whether there is enough evidence to conclude that the mean test scores for the two groups were different. Do a suitable statistical test to assess the evidence. Stat the null hypothesis and the alternative hypothesis, and describe the distribution of the test statistic under the null hypothesis. Find the probability value for your result, and state you conclusion clearly.

Old Method New Method

11 13

14 16

21 25

26 33

25 31

22 29

15 20

26 33

22 27

20 25

31 38

32 23

15 30

25 29

23 24

19

a) Histograms for the two data sets are presented below. Comment on whether it seems justified to assume scores are from normal distributions with equal standard deviations.

Old Method Bin Frequency

Bins 14 2

14 19 3

19 24 5

24 29 4

29 34 2

34 More 0

New Method Bin Frequency

14 14 1

19 19 1

24 24 3

29 29 5

34 34 4

39 More 1

b) Summary statistics for the two data sets are as follows

Mean Standard n

Deviation

Old Method 21.69 5.93 15

New Method 26.40 6.65 16

The teacher wishes to investigate whether there is enough evidence to conclude that the mean test scores for the two groups were different. Do a suitable statistical test to assess the evidence. Stat the null hypothesis and the alternative hypothesis, and describe the distribution of the test statistic under the null hypothesis. Find the probability value for your result, and state you conclusion clearly.

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