A newspaper vendor in Singapore is trying to predict how many copies of The Straits Timesthey 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 FridayNumber of copies sold 74 97 91 86 112A goodness of fit test at the 5 % significance level is used on this data to determine whetherthe vendor’s model is suitable. The critical value for the test is 9.49.(a) Find an estimate for how many copies the vendor expects to sell each day. [1](b) (i) State the null and alternative hypotheses for this test
Question
A newspaper vendor in Singapore is trying to predict how many copies of The Straits Timesthey 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 FridayNumber of copies sold 74 97 91 86 112A goodness of fit test at the 5 % significance level is used on this data to determine whetherthe vendor’s model is suitable. The critical value for the test is 9.49.(a) Find an estimate for how many copies the vendor expects to sell each day. 1 (i) State the null and alternative hypotheses for this test
Solution
(a) To estimate how many copies the vendor expects to sell each day, we need to find the average number of copies sold in a week. We do this by adding up the total number of copies sold from Monday to Friday and then dividing by the number of days (5).
Total copies sold = 74 (Monday) + 97 (Tuesday) + 91 (Wednesday) + 86 (Thursday) + 112 (Friday) = 460 copies
Average copies sold per day = Total copies sold / Number of days = 460 / 5 = 92 copies
So, the vendor expects to sell an estimated 92 copies each day.
(b) (i) The null and alternative hypotheses for this test are:
Null Hypothesis (H0): The vendor's model is correct, and the number of copies sold each day is the same.
Alternative Hypothesis (H1): The vendor's model is not correct, and the number of copies sold each day is not the same.
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