Answer:
The calculated χ² = 0.842 does not fall in the critical region χ² ≥ 5.99 so we accept the null hypothesis that all the proportions are equal and there is not enough evidence to doubt the supermarket's claim.
Step-by-step explanation:
1) We set up our null and alternative hypothesis as
H0: p1= 5/18, p2= 4/18, p3= 9/18
against the claim
Ha: p1≠ 5, p2≠ 4, p3≠ 9
2) the significance level alpha is set at 0.05
3) the test statistic under H0 is
χ²= ∑ (O - E)²/ E where O is the observed and E is the expected frequency
which has an approximate chi square distribution with 2 d.f
4) Computations:
Observed Expected χ²= ∑ (O - E)²/ E
5 5.4 0.0296
4 5.4 0.3629
9 7.2 0.45
∑ 0.842
5) The critical region is χ² ≥ χ² (0.05)2 = 5.99
6) Conclusion:
The calculated χ² = 0.842 does not fall in the critical region χ² ≥ 5.99 so we accept the null hypothesis that all the proportions are equal and there is not enough evidence to doubt the supermarket's claim.
