Question

The Quality Assurance Officer for DagWorths Supermarket is responsible for ensuring prepackaged apples comply with their marked weights. They routinely inspect prepacked apples to determine if the contents of the 5 kg bags of apples weigh at least the 5 kilograms advertised. A random sample of 80 bags, whose advertised weight claims to be 5 kg, yielded the following statistics: X-5.53 S 0.52 (a) Construct a 95% confidence interval estimate for the mean weight of a bag of pre-packaged apples. Hint: Clearly justify the choice of the sampling distribution of the sample mean. Include the steps of the confidence interval estimation and appropriate critical values. (b) Interpret the estimated confidence interval obtained in (a)

Answer 1

a)

sample std dev ,    s =    0.52
Sample Size ,   n =    80
Sample Mean,    x̅ =   5.53

Ho :   µ =   5
Ha :   µ ╪   5

degree of freedom=   DF=n-1=   79
't value='   tα/2=t_0.05/2= 1.9905
      
Standard Error , SE =   s/√n =   0.0581
margin of error ,   E=t*SE =   0.1157

95% confidence interval is       
Interval Lower Limit=   x̅ - E =    5.4143
Interval Upper Limit=   x̅ + E =    5.6457

since ,the confidence interval does not zero, so, reject Ho
b)

we are 95% confident that population mean weight of a bag of pre-pakaged apples lies in the interval(5.41,5.64)kg