Question

The weights of four randomly and independently selected bags of tomatoes labeled 5.0 pounds were found to be 5.3, 5.0, 5.6, and 5.4 pounds. Assume Normality. Answers part (a) and (b) below.

(a). Find a 95% confidence interval for the mean weight of all bags of tomatoes. (__,__)

(b). Does the interval capture 5.0 pounds? Is there enough evidence to reject a mean weight of 5.0 pounds? Explain.

Answer 1

From the sample data,

Sample mean = X / n

= 21.3/4

= 5.325

Standard deviation s = Sqrt ( X² - n ² / n-1)

= sqrt ( 90.81 - 4 * 5.325² / 3)

= 0.25

a)

t critical value at 0.05 significance level with 3 df = 3.182

95% confidence interval for is

- t * S / sqrt(n ) < <   + t * S / sqrt(n )

5.325 - 3.182 * 0.25 / sqrt(4) < < 5.325 + 3.182 * 0.25 / sqrt(4)

4.927 < < 5.723

95% CI is ( 4.927 , 5.723 )

b)

Yes, confidence interval does contains 5.

We do not have sufficient evidence to reject a mean weight of 5 pounds.