The weights of four randomly and independently selected bags of tomatoes labeled 5.0 pounds were found...

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The weights of four randomly and independently selected bags of tomatoes labeled 5.0 pounds were found...

The weights of four randomly and independently selected bags of tomatoes labeled 5.0 pounds were found to be 5.4, 5.0, 5.3, and 5.5 pounds. Assume Normality. Answer parts (a) and (b) below.

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

b. Can you reject the population mean of 5 pounds?

math Statistics-And-Probability

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Answer 1

Answer #1

sample mean, xbar = 5.3
sample standard deviation, s = 0.216
sample size, n = 4
degrees of freedom, df = n - 1 = 3

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, tc = t(α/2, df) = 3.182

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (5.3 - 3.182 * 0.216/sqrt(4) , 5.3 + 3.182 * 0.216/sqrt(4))
CI = (4.96 , 5.64)

b)
can not reject the population mean of 5 pounds

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Answer 2

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