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The graph below shows the amount of salt, in grams, purchased per person per week in England between 2001–02 and 2014, based upon the Large Data Set - AQA - A-Level Maths Mechanics - Question 16 - 2019 - Paper 3

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Question 16

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The graph below shows the amount of salt, in grams, purchased per person per week in England between 2001–02 and 2014, based upon the Large Data Set. Meera and Gemm... show full transcript

Worked Solution & Example Answer:The graph below shows the amount of salt, in grams, purchased per person per week in England between 2001–02 and 2014, based upon the Large Data Set - AQA - A-Level Maths Mechanics - Question 16 - 2019 - Paper 3

Step 1

Give two reasons why Gemma may be correct.

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Answer

  1. The scale on the y-axis does not start at zero, which can exaggerate the perceived decline in salt consumption. This visual distortion may lead to misleading interpretations of the data.

  2. The data presented in the graph only reflects salt purchased, not consumed. Therefore, it may not represent actual changes in dietary salt intake, as purchases do not always equate to consumption.

Step 2

State both hypotheses correctly for two-tailed test.

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Answer

Null Hypothesis ( H_0 ext{): } ext{population mean is } 78.9

Alternative Hypothesis ( H_1 ext{): } ext{ } ar{x} eq 78.9

Step 3

Formulate the test statistic or use the correct distribution of the sample.

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To find the test statistic, we use the formula:

oindent ext{Test Statistic} = rac{ar{x} - ext{population mean}}{ ext{Standard Deviation /} ext{√n}}

Substituting the values gives:

rac{80.4 - 78.9}{25.0 / ext{√918}} = 1.82

Step 4

Obtain the correct value of the test statistic.

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The computed test statistic is 1.82.

Using the standard normal distribution, the critical value for a two-tailed test at a 5% level of significance is approximately 1.96.

Step 5

Compare the test statistic with the critical value.

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Since 1.82 < 1.96, we do not reject the null hypothesis

This indicates that there is insufficient evidence to suggest that the mean amount of sugar purchased has changed between 2014 and 2018.

Step 6

Explain significance level in context.

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Answer

At the 10% significance level, if the null hypothesis is rejected, it indicates there is a 10% chance of rejecting a true null hypothesis.

This means that while we have evidence suggesting a change, it’s not definitive; there remains a chance that what we observed could be due to random variation.

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