Are there differences in airfare depending on which travel agency website you utilize? The following data were collected on travel agency websites on July
9
,

2
0
1
8
.
The following table contai

Question

Are there differences in airfare depending on which travel agency website you utilize? The following data were collected on travel agency websites on July 
9
,
 
2
0
1
8
.
 ﻿The following table contains the prices in U
.
S
.
 ﻿dollars for a one
-
way ticket between the otiles listed on the left for 
2
 ﻿ich of the three travel agency websites. Here the pairs of cltles are the blocks and the treatments are the different websites. Click on the datafile logo to reference the data.
DATA
His
\
table
[
[
,
Websites
]
,
[
Flight From 
-
 ﻿To
,
Expedia 
(
$
)
,
TripAdvisor 
(
$
)
,
Priceline 
(
$
)
]
,
[
Atlanta to Seattle,
3
0
0
,
1
9
8
,
3
4
7
]
,
[
New York to Los Angeles,
3
3
7
,
2
7
4
,
3
5
2
]
,
[
Cleveland to Orlando,
4
2
,
5
1
,
6
0
]
,
[
Dallas to Indianapolis,
1
7
9
,
2
0
2
,
1
7
1
]
]
Use 
α
=
0
.
0
5
 ﻿to test for any significant differences in the mean price of a one
-
way airline tioket for the three travel agency websites. If your answer is zero, enter 
"
 
0
 
"
.
\
table
[
[
Source of variation,SS 
(
to 
2
 ﻿decimals
)
,
d
f
,
MS 
(
to 
2
 ﻿decimals
)
,
,
F
 
(
to 
2
 ﻿decimas
)
,
P
-
value 
(
to 
4
 ﻿decimals
)
,
Fcrit 
(
to 
4
 ﻿decimals
)
]
,
[
Trip
,
9
6
8
0
4
.
9
2
,

VIPSolutions · Accepted Answer

Let's clarify your question and walk through the **Randomized Block ANOVA** for this dataset.

### **Data Table Recap**

| Flight From-To           | Expedia ($) | TripAdvisor ($) | Priceline ($) |
|------------------------- |------------|-----------------|---------------|
| Atlanta to Seattle       |     300    |      198        |     347       |
| New York to Los Angeles  |     337    |      274        |     352       |
| Cleveland to Orlando     |      42    |       51        |      60       |
| Dallas to Indianapolis   |     179    |      202        |     171       |

We have **4 blocks (routes)** and **3 treatments (websites)**.

---

## **ANOVA Table (some values given, others to be filled)**

| Source         | SS        | df   | MS        | F       | P-value  | Fcrit   |
|----------------|-----------|------|-----------|---------|----------|---------|
| Trip (Block)   | 96804.92  | 3    | 32268.31  | 27.91   |          | 4.7571  |
| Website        | 2841.50   | 2    | 1420.75   | 0       | 5.1433   |
| Error          | 6935.83   | 6    | 1155.97   |         |          |         |
| Total          |106582.25  | 11   |           |         |          |         |

Note: Some values are missing and need to be filled in.

---

## **Let’s Fill in the Missing Values:**

### 1. **Degrees of Freedom (df):**
- **Trip (Block):** $ t-1 = 4-1 = 3 $
- **Website:** $ k-1 = 3-1 = 2 $
- **Error:** $ (t-1)(k-1) = 3 \times 2 = 6 $
- **Total:** $ N-1 = 12-1 = 11 $ (since there are 4 routes × 3 websites = 12 data points)

---

### 2. **Mean Square (MS):**
- **Trip (Block):** $ MS_{Trip} = SS_{Trip} / df_{Trip} = 96804.92/3 = 32268.31 $
- **Website:** $ MS_{Website} = SS_{Website} / df_{Website} = 2841.50/2 = 1420.75 $
- **Error:** $ MS_{Error} = SS_{Error} / df_{Error} = 6935.83/6 = 1155.97 $

---

### 3. **F-statistic (for Website):**
- $ F = MS_{Website} / MS_{Error} = 1420.75/1155.97 = \textbf{1.229} $

---

### 4. **P-value for Website:**
- With $ df_1 = 2 $, $ df_2 = 6 $, and $ F = 1.23 $

Looking up in an F-table or using a calculator:
- The p-value for F = 1.23, df1 = 2, df2 = 6 is **about 0.358**.

---

### 5. **Critical F-value (Fcrit) at $\alpha = 0.05$:**
- $ df1 = 2 $, $ df2 = 6 $, $ F_{0.05,2,6} \approx 5.1433 $ (given in your table).

---

## **Final ANOVA Table (Filled):**

| Source         | SS        | df   | MS        | F       | P-value | Fcrit   |
|----------------|-----------|------|-----------|---------|---------|---------|
| Trip (Block)   | 96804.92  | 3    | 32268.31  | 27.91   |         | 4.7571  |
| Website        | 2841.50   | 2    | 1420.75   | 1.23    | 0.358   | 5.1433  |
| Error          | 6935.83   | 6    | 1155.97   |         |         |         |
| Total          |106582.25  | 11   |           |         |         |         |

---

## **Interpretation**

- **p-value for Website = 0.358**
- Since $ p $ is **much greater than 0.10**, there is **no statistically significant difference** in the mean prices among the three websites at the 5% significance level.

---

## **Answer to the Question**

> The p-value corresponding to Website is ◻ greater than 0.10

**Fill in the blank:**
- **greater than**

**So, the p-value corresponding to Website is greater than 0.10.**

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