Solved: A newspaper vendor in Singapore is trying to predict how many copies of The... [IB Mathematics Applications & Interpretation (Math AI)]

Question

SLPaper 1

A newspaper vendor in Singapore is trying to predict how many copies of The Straits Times they will sell. The vendor forms a model to predict the number of copies sold each weekday. According to this model, they expect the same number of copies will be sold each day. To test the model, they record the number of copies sold each weekday during a particular week. This data is shown in the table. | Day | Monday | Tuesday | Wednesday | Thursday | Friday | | Number of copies sold | 74 | 97 | 91 | 86 | 112 | A goodness of fit test at the 5% significance level is used on this data to determine whether the vendor's model is suitable. The critical value for the test is 9.49 and the hypotheses are H₀: The data satisfies the model. H₁: The data does not satisfy the model.

Find an estimate for how many copies the vendor expects to sell each day.

[1]

Verified

Solution

$\left(\frac{74+97+91+86+112}{5}\right)=92$ A1 [1 mark]

Write down the degrees of freedom for this test.

[1]

Verified

Solution

4 A1

Write down the conclusion to the test. Give a reason for your answer.

[4]

Verified

Solution

$\chi_{\text{calc}}^2=8.54(8.54347\ldots)$ OR $p$ -value $=0.0736(0.0735802\ldots)$ A2 8.54<9.49 OR $0.0736>0.05$ R1 therefore there is insufficient evidence to reject $H_0$ A1 (i.e. the data satisfies the model)

Note: Do not award R0A1. Accept "accept" or "do not reject" in place of "insufficient evidence to reject". Award the R1 for comparing their $p$ -value with 0.05 or their $\chi^2$ value with 9.49 and then FT their final conclusion.

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