In: Statistics and Probability
A representative sample of 35 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, 16 selected plain, 12 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.
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
## We have to use MINITAB and do chi square goodness of fit :
here total observation = 35
MINITAB c1 : Sandwich and c2 = count
Stat > table > chi square goodness of fit > observed count select count ( c2 )
> categorical count select count (c2)
## Step 1: State hypotheses and check assumptions
Answer :
Ho : all proportion are equal vs
H1 : not all proportion are equal
we can use chi square goodness of fit because we have one variable and it is categorical :
it is necessary to do chi square test ( assumption )
Step 2: Compute the test statistic
Answer : chi square = 3.48571
Step 3: Determine the p-value
Answer : 0.175
Step 4: Decide to reject or fail to reject the null hypothesis
Decision : we reject Ho if p value is less than α value using p value approach here p value is > α
value we fail to reject Ho at given level of significance .
Step 5: State a real-world conclusion
There is Insufficient evidence that the proportions of people in the population who would choose plain , everything and sesame bagels are not equal .
( ie proportions are equal )
## Output of the chi square goodness of fit :
MTB > TChiSquare;
SUBC> Observed 'count';
SUBC> GBar;
SUBC> GChiSQ;
SUBC> Pareto;
SUBC> RTable.
Chi-Square Goodness-of-Fit Test for Observed Counts in Variable:
count
Test Contribution
Category Observed Proportion Expected to Chi-Sq
1 16 0.333333 11.6667 1.60952
2 12 0.333333 11.6667 0.00952
3 7 0.333333 11.6667 1.86667
N DF Chi-Sq P-Value
35 2 3.48571 0.175