Question

1. Advertisements claim that Happy Joe's puts more pepperoni on its pizzas than competitors. In order to investigate this claim, 9 medium pizzas from Happy Joe's and 9 medium pizzas from Pizza Hut are purchased at random times over a month long period.  The number of slices of pepperoni on each pizza is then counted. At , can you support the claim?
2. Perform the hypothesis test.
   1. Check Conditions
      State Work here
   2. Hypotheses
      State Work here
   3. Statistic
      State Work here
   4. Critical Value(s)
      State Work here
   5. Test Statistic
      State Work here
   6. P-Value
      State Work here
   7. Decision
      State Work here
   8. Conclusion
      State Work here

Happy Joe’s	25	20	21	24	23	24	26	25	21
Pizza Hut	18	22	18	19	18	22	21	19	20

Answer 1

From the Data:

For Weight Lifting: = 23.22, s₁ = 2.108, n₁ = 9

For Cardio: = 19.67, s₂ = 1.658, n₂ = 9

(i) Conditions:

(a) Sampling is a simple random sample

(b) samples are independent

(c) Assumed to be from populations that are approximately normal

(ii) Hypothesis:

H0: = : The mean amount of pepperoni in Joes Pizzas is equal to the mean amount of pepperoni in Pizza Hut.

Ha: > : The mean amount of pepperoni in Joes Pizzas is greater than the mean amount of pepperoni in Pizza Hut.

(iii) The Test Statistic to be used is the t statistic for 2 independent samples.

(iv) Critical Value: For Right tail at = 0.05, df = n1 + n2 - 2 = 16 is 1.746

(v) Test Statistic:

We use the pooled variance as s1/s2 = 1.27 (it lies between 0.5 and 2)

(vi) The p value, Right tail at t = 3.97, degrees of freedom = 8 is 0.0005

(vii) The Decision:

Since t observed (3.97) is > tcritical (1.7460, We Reject H0.

Also, since the p value (0.0005) is < (0.05), We Reject H0.

(viii) The Conclusion: There is sufficient evidence at the 0.05 level of significance to conclude that the mean amount of pepperoni in Joes Pizzas is greater than the mean amount of pepperoni in Pizza Hut.