Question

1. Chi-Square Goodness-of-Fit Test A representative sample of 37 customers at bagel shop were surveyed and ask if they prefer sandwiches made on plain, everything, or sesame bagels. Each participant could only select their one most favorite bagel type. In that sample, 17 selected plain, 13 selected everything, and 7 selected sesame. Conduct a chi-square goodness-of-fit test to determine if there is evidence that the proportions of people in the population who would choose plain, everything, and sesame bagels are not all equal. Use Minitab Express and remember to include all relevant output. [25 points] Step 1: State hypotheses and check assumptions Step 2: Compute the test statistic Step 3: Determine the p-value Step 4: Decide to reject or fail to reject the null hypothesis Step 5: State a real-world conclusion.

Answer 1

Category	Observed(O)	Proportion, p	Expected Frequency (E)	(O-E)²/E
Plain	17	1/3	37 * 1/3 = 12.333	(17 - 12.333)²/12.333 = 1.7659
Everything	13	1/3	37 * 1/3 = 12.333	(13 - 12.333)²/12.333 = 0.036
Sesame	7	1/3	37 * 1/3 = 12.333	(7 - 12.333)²/12.333 = 2.3062
Total	37	1.00	37	4.1081

1. Null and Alternative hypothesis:

Ho: Proportions are same.

H1: Proportions are different.

2. Test statistic:

χ² = ∑ ((O-E)²/E) = 4.1081

3. df = n-1 = 2

p-value = CHISQ.DIST.RT(4.1123, 2) = 0.1279

4. Decision:

p-value > α, Do not reject the null hypothesis

5. Conclusion:

There is not enough evidence to conclude that the proportions of people in the population who would choose plain, everything, and sesame bagels are not all equal.