Question

In 1998, as an advertising campaign, the Nabisco Company announced a “1000 Chips Challenge,” claiming that every 18-ounce bag of their Chips Ahoy cookies contained at least 1000 chocolate chips. Dedicated Statistics students at the Air Force Academy (no kidding) purchased some randomly selected bags of cookies, and counted the chocolate chips. Some of their data are given below. (Chance, 12, no. 1[1999])

1219   1214   1087   1200   1419   1121   1325   1345

1244   1258   1356   1132   1191   1270   1295   1135

a) Write appropriate hypotheses.

b) Are the necessary assumptions to make inferences satisfied? Hint: draw a picture

c) State the sample mean, standard error, and p-value.

d) State an appropriate conclusion.

e) What do you think of the company’s claim?

Answer 1

a)

Ho :   µ =   1000
Ha :   µ >   1000
...............

sample std dev ,    s = √(Σ(X- x̅ )²/(n-1) ) =   94.2820  
Sample Size ,   n =    16  
Sample Mean,    x̅ = ΣX/n =    1238.1875  
          
degree of freedom=   DF=n-1=   15  
          
Standard Error , SE = s/√n =   94.282/√16=   23.5705  
t-test statistic= (x̅ - µ )/SE =    (1238.1875-1000)/23.5705=   10.105  
          
          
p-Value   =   0.0000   [Excel formula =t.dist(t-stat,df) ]

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

Decision:   p-value≤α, Reject null hypothesis   
Conclusion: There is enough evidence to say that mean cheaps is greater than 1000

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

company's claim is supported

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

thanks

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