Question

A research article on whether the taste of coffee is influenced by the color of the mug describes an experiment in which subjects were assigned at random to one of two treatment groups. The 14 people in one group were served coffee in a white mug and were asked to rate the quality of the coffee on a scale from 0 to 100. The 14 people in the second group were served the same coffee in a clear glass mug, and they also rated the coffee. The mean quality rating for the 14 people in the white mug group was 50.45 and the standard deviation was 20.88. The mean quality rating for the 14 people in the clear glass mug group was 61.99 and the standard deviation was 16.37. For purposes of this exercise, you may assume that the distribution of quality ratings for each of the two treatments is approximately normal. (a) Use the given information to construct a 95% confidence interval for the difference in mean quality rating for this coffee when served in a white mug and when served in a glass mug. (Use - u glass mug' Use a table or technology. Round your answers to two decimal places.) M white mug Interpret the interval. We are 95% confident that the difference in mean quality rating for the coffee tasted in this experiment when served in a white mug and when served in a glass mug falls within this interval. O There is a 95% chance that the difference in mean quality rating for the coffee tasted in this experiment when served in a white mug and when served in a glass mug falls within this interval. There is a 95% chance that the difference in mean quality rating for the coffee tasted in this experiment when served in a white mug and when served in a glass mug falls directly in the middle of this interval. O There is a 95% chance that the true difference in mean quality rating for this coffee when served in a white mug and when served in a glass mug falls directly in the middle of this interval. We are 95% confident that the true difference in mean quality rating for this coffee when served in a white mug and when served in a glass mug falls within this interval. (b) Based on the interval from part (a), are you convinced that the color of the mug makes a difference in terms of mean quality rating? Explain. The confidence interval ---Select--- to conclude that the color of the mug makes a difference in terms of mean quality rating because zero ---Select--- V included in the confidence interval.

Answer 1

a)

Sample #1   ---->   White
mean of sample 1,    x̅1=   50.45              
standard deviation of sample 1,   s1 =    20.88              
size of sample 1,    n1=   14              
                      
Sample #2   ---->   Clear   
mean of sample 2,    x̅2=   61.99              
standard deviation of sample 2,   s2 =    16.37              
size of sample 2,    n2=   14              
                      
difference in sample means =    x̅1-x̅2 =    50.4500   -   62.0   =   -11.54

Degree of freedom, DF=   n1+n2-2 =    26              
t-critical value =    t α/2 =    2.0555   (excel formula =t.inv(α/2,df)          
                      
pooled std dev , Sp=   √([(n1 - 1)s1² + (n2 - 1)s2²]/(n1+n2-2)) =    18.7610              
                      
std error , SE =    Sp*√(1/n1+1/n2) =    7.0910              
margin of error, E = t*SE =    2.0555   *   7.0910   =   14.5758  
                      
difference of means =    x̅1-x̅2 =    50.4500   -   61.990   =   -11.5400
confidence interval is                       
Interval Lower Limit=   (x̅1-x̅2) - E =    -11.5400   -   14.5758   =   -26.12
Interval Upper Limit=   (x̅1-x̅2) + E =    -11.5400   +   14.5758   =   3.04

We are 95% confident that the true difference in mean quality rating for this coffee when served in a white mug and when served in a glass mug falls within this interval.

2)

Color does not make a difference

because confidence interval contain 0

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