Question

Boston Bottling Company distributes cola in cans labeled 12 oz The mean of 11.82 oz and a randomly selected 24 cans, measured their Bureau of Weights and Measures contents, and obtained a sample mean of 11.82 of 38 oz. Use a 01 sample standard deviation is cheating nicance level to test the claim that the company Use the Traditional is less than 12 oz. consumers, Le that the average content Method. Assume the population is ted Claim (in words) a) Ho b) Critical value(s) c) Test value d) Decision (reject/fail to reject Ho) e) Wording in terms of claim

Answer 1

From the given information,

Sample size (n) = 24, sample mean (xbar) = 11.82 oz. , Sample standard deviation (s) = 0.38

Here we conduct one sample t test because population standard deviation is unknown.

The claim is the average content of cola in can is less than 12 oz.

1. The hypotheses are

H₀:µ = 12 oz.

H₁:µ < 12 oz.

2. T critical value for one tailed with α=0.01 and degrees of freedom = n-1 = 24 – 1 = 23 is t_23,0.01 = -2.500

Rejection region: reject H₀ if t < -2.500.

3. Test statistics (t) = (X - µ) / (S/ √n)

T = (11.82 - 12) / (0.38/sqrt(24))

Test value t = -2.32

4. Test statistics t = -2.32 > t_23.0.01 = -2.50 so we failed to reject H₀.
5. Conclusion: There is no sufficient evidence at α = 0.01 level of significance to claim that the average content of cola in can is less than 12 oz.