# Statistics Question 4

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Question 4. [ 23 marks ] [Second half of Chapter 8]

We wish to investigate whether, on average, the sodium (salt) content of breakfast cereals

depends on the manufacturer: Hubbards, Kellogg’s and Sanitarium. Three random samples each of

20 breakfast cereals on sale in New Zealand were collected from the three manufacturers and the

sodium content (in milligrams per 100 grams of cereal) was recorded.

Note:

Excel, CerealINZIGHT, and SPSS, CerealSPSS, files of the data are available on Canvas

Assignment 3.®on the Home Page or look under Assignments

(a) For this study describe the: [ 1 mark ]

(i) units,

(ii) treatment or factor of interest,

(iii) response.

(b) (i) Use iNZight to draw the appropriate plots(s) for this data set.

(ii) Comment on any features in the plot(s) in terms of the original story. [ 3 marks ]

(c) Using SPSS, provide the computer output of an F‐test on these data. [ 1 mark ]

Notes:

• Refer to the SPSS Tutorial, Pages 16 and 17, on Canvas. (Look under Software Information

SPSS Help.)®and Help

• Ensure that you complete Step 1 through to Step 4 of the instructions on Pages 16 and 17.

(d) State the assumptions of the F‐test in terms of the original story. [ 4 marks ]

(e) Calculate the ratio of the largest sample standard deviation for the sodium content to the

smallest sample standard deviation for the sodium content.

(Note: The ratio of A to B is A divided by B.) [ 1 mark ]

(f) Comment on the validity of the F‐test by briefly discussing each assumption. [ 3 marks ]

(g) Assume that an F‐test is an appropriate test to use here. (Note: It may not be.)

(i) State the null hypothesis for the test, both in words and using symbols. [ 1 mark ]

(ii) State the alternative hypothesis for the test in words. [ 1 mark ]

(iii) What does the result of the F‐test tell you about the underlying mean sodium content

for the three manufacturers? Explain your answer in 1 to 2 sentences. [ 1 mark ]

(h) (i) Assume the Tukey’s pairwise comparisons are valid and appropriate.

(Note: they may not be.)

Investigate whether there is a difference between the underlying mean sodium content

of breakfast cereals produced by Sanitarium and that of breakfast cereals produced by

Kellogg’s. Interpret the P‐value and confidence interval.

Note: A conclusion is not required here. [ 2 marks ]

(ii) Between which pair (or pairs) of manufacturers were there significant differences

(at the 5% level) in the underlying mean sodium content of breakfast cereals? [ 1 mark ]

(iii) Are we able to determine which manufacturer has the lowest underlying mean

sodium content of breakfast cereals? If so, name the manufacturer. [ 1 mark ]

(i) In three to five sentences, provide an overall conclusion for this study. [ 3 marks ]

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