Question

I am struggling with answering A,B & C with details

1. The weights of four randomly and independently selected bags of tomatoes labeled 5 pounds were found to be 5.1, 5.0, 5.3, and 5.1 pounds. Assume Normality.
   1. Find a 95% confidence interval for the mean weight of all bags of tomatoes.
   2. Does the interval capture 5.0 pounds? Is there enough evidence to reject a mean weight of 5.0 pounds?
   3. Interpret the above 95% confidence interval for the mean weight of all bags of tomatoes.

Answer 1

a)

From the given sample data,

= X / n = 5.125

S = sqrt [ X2 - n 2 / n-1 ] = 0.1258

95% Confidence Interval
X̅ ± t(α/2, n-1) S/√(n)
t(α/2, n-1) = t(0.05 /2, 4- 1 ) = 3.182
5.125 ± 3.182 * 0.1258/√(4)
Lower Limit = 5.125 - 3.182 * 0.1258/√(4)
Lower Limit = 4.925
Upper Limit = 5.125 + 3.182 * 0.1258/√(4)
Upper Limit = 5.325
95% Confidence interval is ( 4.925 , 5.325 )

b)

Yes, the interval capture 5 pounds.

We do not have sufficient evidence to  reject a mean weight of 5.0 pounds.

c)

Interpretation = We are 95% confident that the true mean weight of all bags of tomatoes is

between 4.925 pounds and 5.325 pounds.