It is considered quite common to have feet of unequal length. In a sample of 10 healthy college students the right-foot and left-foot lengths are given (in mm). Test the claim that, on average, there is a measurable difference between left and right foot length. Length in mm mean 8 Left foot ( 281 258 266 270 274 254 265 250 266 245 262.9 11.1300394328942 x) Right foot (y) d = x - y 281 257 267 269 273 253 265 250 267 245 262.7 11.1758668567587 01 (a) Find the test statistic. 0.23 (b) Test the claim at the 0.05 significance level. Positive critical value: -1 1 1 1 0 0 -1 0 0.2 0.788810637746616 Negative critical value:

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### Investigation of Foot Length Discrepancy in College Students

#### Introduction

It is considered quite common for individuals to have feet of unequal length. In a study involving 10 healthy college students, the lengths of the right and left feet were measured in millimeters (mm).

#### Objective

Test the claim that, on average, there is a measurable difference between the left and right foot lengths.

#### Data

| Length in mm  | Left Foot (x) | Right Foot (y) | \(d = x - y\) |
|---------------|---------------|----------------|---------------|
|               | 281           | 281            | 0             |
|               | 258           | 257            | 1             |
|               | 266           | 267            | -1            |
|               | 270           | 269            | 1             |
|               | 274           | 273            | 1             |
|               | 254           | 253            | 1             |
|               | 265           | 265            | 0             |
|               | 250           | 250            | 0             |
|               | 266           | 267            | -1            |
|               | 245           | 245            | 0             |

- **Mean of Left Foot:** 262.9 mm
- **Mean of Right Foot:** 262.7 mm
- **Standard Deviation (s) for Left Foot:** 11.1300394328942
- **Standard Deviation (s) for Right Foot:** 11.1758668567587
- **Mean Difference (d):** 0.2 mm
- **Standard Deviation of Differences (s):** 0.788810637746616

#### Statistical Analysis

(a) **Find the Test Statistic**
  
The calculated test statistic is **0.23**.

(b) **Hypothesis Testing at 0.05 Significance Level**

- **Positive Critical Value:** [To be filled by user]
- **Negative Critical Value:** [To be filled by user]

The test aims to determine if the mean difference in foot length is statistically significant. By using a t-test for paired data, the hypothesis can be evaluated against the calculated critical values.
Transcribed Image Text:### Investigation of Foot Length Discrepancy in College Students #### Introduction It is considered quite common for individuals to have feet of unequal length. In a study involving 10 healthy college students, the lengths of the right and left feet were measured in millimeters (mm). #### Objective Test the claim that, on average, there is a measurable difference between the left and right foot lengths. #### Data | Length in mm | Left Foot (x) | Right Foot (y) | \(d = x - y\) | |---------------|---------------|----------------|---------------| | | 281 | 281 | 0 | | | 258 | 257 | 1 | | | 266 | 267 | -1 | | | 270 | 269 | 1 | | | 274 | 273 | 1 | | | 254 | 253 | 1 | | | 265 | 265 | 0 | | | 250 | 250 | 0 | | | 266 | 267 | -1 | | | 245 | 245 | 0 | - **Mean of Left Foot:** 262.9 mm - **Mean of Right Foot:** 262.7 mm - **Standard Deviation (s) for Left Foot:** 11.1300394328942 - **Standard Deviation (s) for Right Foot:** 11.1758668567587 - **Mean Difference (d):** 0.2 mm - **Standard Deviation of Differences (s):** 0.788810637746616 #### Statistical Analysis (a) **Find the Test Statistic** The calculated test statistic is **0.23**. (b) **Hypothesis Testing at 0.05 Significance Level** - **Positive Critical Value:** [To be filled by user] - **Negative Critical Value:** [To be filled by user] The test aims to determine if the mean difference in foot length is statistically significant. By using a t-test for paired data, the hypothesis can be evaluated against the calculated critical values.
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