Question

A premium golf ball production line must produce all of its balls to 1.615 ounces in order to

get the top rating (and therefore the top dollar). Samples are drawn hourly and checked. If the

production line gets out of sync with a statistical significance of more than 1%, it must be shut

down and repaired. This hour’s sample of 18 balls has a mean of 1.611 ounces and a standard

deviation of 0.065 ounces. Do you shut down the line?

Answer 1

Let X be the weight of the golf balls in ounces

Data Summary

The null and alternative hypotheses are                  
Ho : μ = 1.615     μ is the population mean weight of the golf balls
Ha : μ ≠ 1.615                  
                  
α = 0.01       1% level of significance          
We use T test since population standard deviation is unknown, and sample size is small                  
Using the below formula, we get the test statistic                  
                  
Degrees of Freedom                  
df = n - 1 = 18 - 1 = 17                  
                  
t-statistic      

           
t-statistic =                     
                  
For t = -0.2611 df = 17 we find the Two Tailed p-value using Excel function t.dist                                   
p-value = 2 * t.dist(-0.2611, 17, TRUE)                  
p-value =        
                  
Decision                  
0.7972 > 0.01                  
that is p-value > α                  
Hence we DO NOT REJECT Ho                
                  
Conclusion                  
There does not exist enough statistical evidence at 1% level of significance to show that the mean weight of the golf balls is not 1.615 ounces

that is,

The mean weight is 1.615 ounces and hence the line should not be shut down

-------------------------------------------------------------------------------------------------------------------------------------------

If you are satisfied with the solution, kindly give a thumbs up.