Statistical Truth or Fiction: Debunking the Myths

The scale from 0 to 10 (where 0 strongly dislikes and 10 is strongly like) can be represented as below; 

Assuming that Marjin -O Heara should only recommend the production of new jerseys if the color is at least liked by the fans. We have to test whether the information obtained from the sample suggest that the fans like the selected color. We therefore test the null hypothesis that the mean rating is equal to 8. 

Null hypothesis: M ean rating of fans = 8, ( H 0: μ=8) 

Alternative hypothesis: M ean rating of fans = 8 ( 

Sample mean,  =6.5, sample standard deviation, s = 0.04, sample size, n= 400, assumed population mean that means the color strongly liked, = 8 

We use z-test since the sample is 

We calculate z-statistic using the formula 

Z-statistic, Z = 

Z =  = -750 

Z statistic = -750 

Assuming 0.05 level of significance we read  from z-tables 

Lowe tail  = 1.645 

Decision rule 

Reject null hypothesis if Z  1.645 

Conclusion 

Since -750 < 1.645, we reject the null hypothesis and conclude that there exists insufficient statistical evidence to conclude that the population mean rating by fans is 8. This means that Marjin -O Heara should NOT recommend the production of new jerseys because the color is not liked by the fans.