Question

Do college students enjoy playing sports more than watching sports? A researcher randomly selected ten college students and asked them to rate playing sports and watching sports on a scale from 1 to 10 with 1 meaning they have no interest and 10 meaning they absolutely love it. The results of the study are shown below. Playing Vs. Watching Sports Play 9 1 6 1 2 6 3 2 1 8 Watch 6 1 4 1 1 5 3 1 1 8 Assume a Normal distribution. What can be concluded at the the α = 0.05 level of significance level of significance? For this study, we should use The null and alternative hypotheses would be: H 0 : (please enter a decimal) H 1 : (Please enter a decimal) The test statistic = (please show your answer to 3 decimal places.) The p-value = (Please show your answer to 4 decimal places.) The p-value is α Based on this, we should the null hypothesis. Thus, the final conclusion is that ... The results are statistically insignificant at α = 0.05, so there is insufficient evidence to conclude that the population mean rating for playing sports is greater than the population mean rating for watching sports. The results are statistically insignificant at α = 0.05, so there is statistically significant evidence to conclude that the population mean rating for playing sports is equal to the population mean rating for watching sports. The results are statistically significant at α = 0.05, so there is sufficient evidence to conclude that the ten students that were surveyed rated playing sports higher than watching sports on average. The results are statistically significant at α = 0.05, so there is sufficient evidence to conclude that the population mean rating for playing sports is greater than the population mean rating for watching sports.

Answer 1

Ho :   µ1 - µ2 =   0                  
Ha :   µ1-µ2 >   0                 
                          
Level of Significance ,    α =    0.05                  
                          
Sample #1   ---->   sample 1                  
mean of sample 1,    x̅1=   3.90                  
standard deviation of sample 1,   s1 =    3.07                  
size of sample 1,    n1=   10                  
                          
Sample #2   ---->   sample 2                  
mean of sample 2,    x̅2=   3.10                  
standard deviation of sample 2,   s2 =    2.56                  
size of sample 2,    n2=   10                  
                          
difference in sample means =    x̅1-x̅2 =    3.9000   -   3.1   =   0.80  
                          
pooled std dev , Sp=   √([(n1 - 1)s1² + (n2 - 1)s2²]/(n1+n2-2)) =    2.8265                 
std error , SE =    Sp*√(1/n1+1/n2) =    1.2640                  
                          
t-statistic = ((x̅1-x̅2)-µd)/SE = (   0.8000   -   0   ) /    1.26   =   0.633
                          
Degree of freedom, DF=   n1+n2-2 =    18                  

p-value =        0.2674   [excel function: =T.DIST.RT(t stat,df) ]              
Conclusion:     p-value>α , Do not reject null hypothesis                     

Thus, the final conclusion is that ... The results are statistically insignificant at α = 0.05, so there is insufficient evidence to conclude that the population mean rating for playing sports is greater than the population mean rating for watching sports

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