1. Write the conclusion about differences in mean vitamin prices between the four retail outlets. Use the confidence level and comment on which outlets are different and which are similar?

2. Which outlets are the least and most expensive? Be sure to present the most and least expensive outlets in groups, if appropriate.

3. Can we conclude that at least one type of vitamin/supplement (blocks) mean price differs from the others? How much evidence is there to support your conclusion? Please conduct a 5-step hypothesis test.

Please use the information below to answer the questions above:

= .05

• The critical value of the test at the 0.05 level of significance is 2.70.

  From the given Tukey simultaneous comparison t-value for comparing mean prices between retail outlets, the t-values of the test for pairwise comparison that is greater than the critical value 2.70 are:

  - Pairwise comparison between CVS against Walgreens with t-value=3.92, and

  - Pairwise comparison between CVS against Target with t-value=3.92.

  Hence, there is sufficient evidence to conclude that the CVS retail outlet has a significant mean price with the Walgreens and Target outlets.

Thank you!

Tukey simultaneous comparison t-values (d.f. = 36) Walgreens Target Rite-Aid CVS 9.82385 9.92692 10.30923 10.93154 Walgreens 9.82385 Target 9.92692 0.40 Rite-Aid 10.30923 1.89 1.49 CVS 10.93154 4.32 3.92 2.43 critical values for experimentwise error rate: 0.05 2.70 0.01 3.35 Item Caltrate +D (600mg/60 tablets) Centrum (130 tablets) Cod liver oil (100 gel tablets) Fish oil (1,000 mg, 60 tablets) Flintstones Children's (60 tablets) Folic acid (400 mcg/250 tablets) One-a-Day Maximum (100 tablets) One-a-Day Scooby (50 tablets) Poly-Vi-Sol (drops, 50 ml.) Vitamin B-12 (100 mcg/100tablets) Vitamin C (500 mg/100tablets) Vitamin E (200 IU/100tablets) Zinc (50 mg/100 tablets) CVS Target 13.49 10.99 14.49 14.47 7.66 7.59 11.19 9.99 12.69 10.99 7.19 7.49 13.99 12.49 12.49 10.99 14.99 13.49 8.59 6.99 7.99 7.49 9.69 8.49 7.66 7.59 Rite-Aid 12.99 14.89 6.99 9.99 10.99 8.74 11.99 11.49 14.99 6.99 6.99 7.99 8.99 Walgreens 10.99 12.97 7.69 10.99 11.29 7.69 11.99 10.47 13.37 6.79 7.39 8.29 7.79 General problem background and purpose: In this exercise we use the data from above to perform a ANOVA analysis (two-factor without replication) that tests whether the retail outlet (treatments) affects the mean price of vitamins and supplements, and whether the type of vitamin/supplement (blocks) affect the mean price across pharmacies. Angva; Two-Factor Without Replication Count 4 4 4 4 4 4 SUMMARY Caltrate +D (600mg/60 tablets) Centrum (130 tablets) Cod liver oil (100 gel tablets) Fish oil (1,000 mg, 60 tablets) Flintstones Children's (60 tablets) Folic acid (400 mcg/250 tablets) One-a-Day Maximum (100 tablets) One-a-Day Scooby (50 tablets) Poly-Vi-Sol (drops, 50 ml.) Vitamin B-12 (100 mcg/100tablets) Vitamin C (500 mg/100tablets) Vitamin E (200 10/100tablets) Zinc (50 mg/100 tablets) Sum 48.46 56.82 29.93 42.16 45.96 31.11 50.46 45.44 56.84 29.36 29.86 34.46 32.03 Average Variance 12.115 1.729167 14.205 0.7153 7.4825 0.109558 10.54 0.41 11.49 0.66 7.7775 0.453958 12.615 0.895833 11.36 0.740933 14.21 0.8136 7.34 0.703333 7.465 0.169167 8.615 0.555833 8.0075 0.435892 4 4 4 4 4 4 4 13 13 8.475281 6.399056 CVS Target Rite-Aid Walgreens 142.11 10.93154 129.05 9.926923 134.02 10.30923 127.71 9.823846 13 8.124808 5.264692 13 ANOVA Source of Variation SS F Rows Columns Error 323.7899 9.801621 15.3761 df MS 12 26.9825 3 3.267207 36 0.427114 63.17399 7.649497 P-value 1.77E-20 0.000443 F crit 2.032703 2.866266 Total 348.9677 51