A chewing gum manufacturer wishes to determine if his customers prefer one flavour of gum to any other flavour.He selects a random sample of customers and records the flavour of gum that is purchased.What
Is the test statistic for the data given?

Question

Quizplus · Accepted Answer

The test statistic for comparing the preferences of two flavours in a sample is the chi-squared statistic. However, since the question does not specify any particular comparison, we assume the null hypothesis is that there is no preference among flavours. The chi-squared statistic for goodness-of-fit test is given by: 
χ² = Σ[(O-E)² / E]
where O is the observed frequency and E is the expected frequency under the null hypothesis. 
We don't have the expected frequencies, but assuming no preference, each flavour should have an equal chance of being chosen, so the expected frequency for each flavour is:
E = (total number of observations) / (number of flavours)
E = n/3, where n is the total number of observations (sample size). 
Therefore, the chi-squared statistic can be calculated as:
χ² = [(44-33.33)²/33.33] + [(28-33.33)²/33.33] + [(28-33.33)²/33.33] 
= 2.395 + 0.555 + 0.555
= 3.50
Using a significance level of 0.05 and degrees of freedom (df) = 3-1 = 2, the critical value from the chi-squared distribution table is 5.99. Since the calculated value (3.50) is less than the critical value (5.99), we fail to reject the null hypothesis that there is no preference among flavours. Therefore, the conclusion is that customers in the sample do not prefer one flavour over another. The test statistic for this hypothesis test would depend on the specific statistical test being used. It is not possible to determine the test statistic without more information.

A Chewing Gum Manufacturer Wishes to Determine If His Customers