Question

1.) Problem: You want to know whether wait times at grocery stores have changed since Sacramento told people to only go out for essential services because of CoVid 19. You decide to test this at the p < .01 level. Grocery stores said their usual wait times to checkout before the virus was 10 minutes, but they don’t know the variance. You randomly select 7 people as they check out and measure their wait time, and find they waited: 9, 9, 10, 14, 13, 12, 13 minutes

1. Restate the question:

   • Population 1:

   • Population 2:

   • Research hypothesis:

   • Null hypothesis

   • Determine the characteristics of the comparison distribution to compare to sample distribution:

     • μ 1 (Population 1):

     • N (Sample 1):

     • df (Sample 1)

     • μ2 (Population 2):

     • S22(Population 2):

     • S2 (Population 2):

     • μ2M (Population 2, distribution of means):

     • σ22M (Population 2, distribution of means):

     • σ2M (Population 2, distribution of means):

c. Determine the critical t-value (cutoff score) on the comparison distribution at which the null hypothesis should be rejected

d. Determine the Z score of your sample

  e. Decide whether to reject the null hypothesis

f. Explain the findings to the average customer who is about to go into the store.

Answer 1

Ho :   µ =   10                  
Ha :   µ ╪   10       (Two tail test)          
                          
Level of Significance ,    α =    0.01                  
sample std dev ,    s = √(Σ(X- x̅ )²/(n-1) ) =   2.0702                  
Sample Size ,   n =    7                  
Sample Mean,    x̅ = ΣX/n =    11.4286                  
                          
degree of freedom=   DF=n-1=   6                 
                          
Standard Error , SE = s/√n =   2.0702   / √    7   =   0.7825      
t-test statistic= (x̅ - µ )/SE = (   11.429   -   10   ) /    0.7825   =   1.83
                          
critical t value, t* =    ±   3.7074   [Excel formula =t.inv(α/no. of tails,df) ]     

      
null hypothesis will be rejected if test stat > 3.7074

here ,

test stat < critical value     
Decision: , Do not reject null hypothesis                       
Conclusion: There is not enough evidence to say that wait times at grocery stores have changed

...............

Please revert back in case of any doubt.

Please upvote. Thanks in advance.