What type of hypothesis?

Question

A teacher wanted to know if her student ice cream preference was different than in previous years. The pie chart below represents the previous percentages. This year, 32 chose vanilla, 31 chose chocolate, 17 chose strawberry, and 6 chose mint chocolate chip. At α=0.05, what can the teacher say? Complete all 7 steps of the hypothesis test.

Pie Chart: 35% Vanilla, 40% Chocolate, 18% Strawbery, 7% Mint Chocolate Chip

Answer 1

There is really insufficient data here to make an answer. For one, texts vary so while one text may break down non parametric goodness of fit tests into 7 steps, another may break it down into 6. This information is needed to be able to generate a full answer.

Also, the type of test is NOT specified. I suggested based on the data a goodness of fit test as this appears the most proper test. Your text may vary.

Third and most important THERE IS NO DATA!

If we assume a chi-squared distribution goodness of fit test the 7 steps should be

1. Step 1: State the Null Hypothesis. Ho: Student ice cream preferences fits previous years distribution
2. Step 2: State the Alternative Hypothesis. Ha: Student ice cream preferences do not fit previous years distribution
3. Step 3: Set alpha. alpha = .05
4. Step 4: Collect Data. [To be done, not given in question. Counts are necessary]
5. Step 5: Calculate a test statistic. .Use standard formula χ²_{=Σ ((Oi - Ei)}² _{/ Ei )}

(note expected values are the given percentages for a flavor times the total number of observed/questioned students in the observation sample. This is done for each flavor and compared in the calculator with the observed counts to get a Xsquared value. )

1. Step 6: Construct Acceptance / Rejection regions. Quickest was is to use Chi Squared calculator to find upper and lower bound given proper counts to develop expected values as well as observed values.
2. Step 7: Based on steps 5 and 6, draw a conclusion about.( if the calculated Xsquare value is less then the lower bound or greater than the upper bound, then the null hypothesis is rejected.