Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim.

A cereal company claims that the mean weight of the cereal in its packets is 14 oz. The weights (in ounces) of the cereal in a random sample of 8 of its cereal packets are listed below.

14.6 13.8 14.1 13.7 14.0 14.4 13.6 14.2

Test the claim at the 0.01 significance level. H₀: the mean weight of the cereal equals 14 oz.; H_a: the mean weight of the cereal equals does not equal 14 oz.; Test statistic Z = 0.6868 and P value = 0.4902; Conclusion: we should reject the null hypothesis.

H₀: the mean weight of the cereal equals 14 oz.; H_a: the mean weight of the cereal does not equal 14 oz.; Test statistic T = 0.4082 and P value = 0.6953; Conclusion: we fail to reject the null hypothesis.

H₀: the mean weight of the cereal does not equal 14 oz.; H_a: the mean weight of the cereal equals 14 oz.; Test statistic T = 0.4082 and P value = 0.6953; Conclusion: we fail to reject the null hypothesis.

H₀: the mean weight of the cereal does not equal 14 oz.; H_a: the mean weight of the cereal equals 14 oz.; Test statistic Z = 0.6868 and P value = 0.4902; Conclusion: we should reject the null hypothesis.