Question

An experiment to compare the spreading rates of five different brands of yellow interior latex paint available in a particular ares used 4 gallons (J=4) of each paint. The sample average spreading rates ( f2/gal) for the five brands were xˉ1.​=462.0,xˉ2​=502.8,xˉ3​=427.5,xˉ4​=469.3, and xˉ5​. =532.1. The computed value of F was found to be significant at level α=0.05. With MSE =480.8, use Tukey's procedure to investigate significant differences between brands. (Round your answer to two decimal places.) w= Which means differ significantly from one another? (Select all that apply.) xˉ3​ and xˉ2​. xˉ1​ and xˉ3​. xˉ1​ and xˉ4​. xˉ1​ and xˉ5​. xˉ2​ and xˉ3​. xˉ2​ and xˉ4​. xˉ2​ and xˉ5​. xˉ3​, and xˉ4​ xˉ3​, and xˉ5​. xˉ4​, and xˉ5​. There are no significant differences. You may need to use the appropriate table in the Appendix of Tables to answer this question.

Answer 1

According to Tukey's procedure, the pairs
`\( \bar{x}_3 \) and \( \bar{x}_2 \), \( \bar{x}_1 \) and \( \bar{x}_5 \), and \( \bar{x}_2 \) and \( \bar{x}_5 \)` exhibit significant differences in spreading rates. Therefore, the correct choices are
`\( \bar{x}_3 \) and \( \bar{x}_2 \), \( \bar{x}_1 \) and \( \bar{x}_5 \), and \( \bar{x}_2 \) and \( \bar{x}_5 \).`

Step-by-step explanation:

Tukey's procedure is a multiple comparison method used to identify significant differences among means in an experiment with a predetermined level of significance. The procedure involves calculating the critical value for the test statistic and comparing it with the differences between means.

Given the sample means
`\( \bar{x}_1, \bar{x}_2, \bar{x}_3, \bar{x}_4, \) and \( \bar{x}_5 \)` and the mean square error (MSE), Tukey's procedure is applied to find significant differences. The critical value for the test statistic is determined based on the number of groups and the degrees of freedom. Comparing the differences between means to the critical value allows identification of pairs with significant differences.

In this case, the calculated critical value indicates that
`\( \bar{x}_3 \) and \( \bar{x}_2 \), \( \bar{x}_1 \) and \( \bar{x}_5 \), and \( \bar{x}_2 \) and \( \bar{x}_5 \)` exhibit significant differences. This information helps in drawing conclusions about the spreading rates of the five paint brands.

Answer 2

The differences between the spreading rates of the five different brands of yellow interior latex paint is xˉ3 and xˉ2 , and xˉ1 and xˉ5

The answer is option ⇒1 and 4

Step-by-step explanation:

To investigate significant differences between the spreading rates of the five different brands of yellow interior latex paint, we can use Tukey's procedure. Tukey's procedure is a statistical method used to determine which means differ significantly from one another.

First, we calculate the critical value for Tukey's procedure using the significance level (α) and the degrees of freedom for the error term (MSE). In this case, the significance level is 0.05 and MSE is given as 480.8.

Next, we calculate the difference between each pair of means and compare it to the critical value. If the difference is greater than the critical value, it means that the means differ significantly.

Let's calculate the differences between each pair of means and compare them to the critical value:

• 1. Difference between xˉ1 and xˉ2: 502.8 - 462.0 = 40.8
• 2. Difference between xˉ1 and xˉ3: 427.5 - 462.0 = -34.5
• 3. Difference between xˉ1 and xˉ4: 469.3 - 462.0 = 7.3
• 4. Difference between xˉ1 and xˉ5: 532.1 - 462.0 = 70.1
• 5. Difference between xˉ2 and xˉ3: 427.5 - 502.8 = -75.3
• 6. Difference between xˉ2 and xˉ4: 469.3 - 502.8 = -33.5
• 7. Difference between xˉ2 and xˉ5: 532.1 - 502.8 = 29.3
• 8. Difference between xˉ3 and xˉ4: 469.3 - 427.5 = 41.8
• 9. Difference between xˉ3 and xˉ5: 532.1 - 427.5 = 104.6
• 10. Difference betweenxˉ4 and xˉ5: 532.1 - 469.3 = 62.8

Now, we compare each difference to the critical value. If the difference is greater than the critical value, it means the means differ significantly.

Using the appropriate table in the Appendix of Tables, we find the critical value for Tukey's procedure with 5 groups and an MSE of 480.8.

After comparing the differences to the critical value, we can conclude that the following means differ significantly from one another:

- xˉ3 and xˉ2

- xˉ1 and xˉ5

Therefore, the correct answer is:

- xˉ3 and xˉ2 (Option 1)

-xˉ1 and xˉ5 (Option 4)