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# Consequently we will use the t distribution to

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greater than 30, and the population is normally distributed. Consequently, we will use the t distribution to perform the test in this exercise. 1. Identify the null hypothesis and alternative hypothesis from a given claim and express both in symbolic form. H : μ=19.8 H : μ ≠19.8 2. Calculate the value of the test statistic, given a claim and sample data x =19.4 ̅ σ = 0.05 s= 1.8 n=40 t= (19.4- 19.8)/(1.8/√40)= -1.4055 3. Identify the critical value(s), given a significance level Critical t value = ± 2.0227 4. Identify the P-value, given a value of the test statistic P-value = 0.1678 5. State the conclusion about a claim in simple and nontechnical terms We believe that you cannot reject the null hypothesis which states that the average coke has 19.8 oz in each bottle. Hypothesis Testing #2 A simple random sample of ten 20-oz bottles of Coke® from a normal distribution is obtained and each bottle is measured for number of ounces of Coke® in the bottle. The sample mean is 19.4 oz with standard deviation of 1.8 oz. Test the claim at an alpha significance level of 5% that on average there is more than 19.8 oz of Coke® in each bottle. The sample size is 10, which is smaller than 30, and the population is normally distributed. Consequently, we will use the t distribution to perform the test in this exercise. 1. Identify the null hypothesis and alternative hypothesis from a given claim and express both in symbolic form. H : µ = 19.8 H : µ > 19.8 2. Calculate the value of the test statistic, given a claim and sample data x =19.4 ̅ σ = 0.05 s= 1.8 n=10 t= (19.4- 19.8)/(1.8/√10)= -0.7027

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3. Identify the critical value(s), given a significance level Critical t value = 1.8331 4. Identify the P-value, given a value of the test statistic P-value = 0.7500 5. State the conclusion about a claim in simple and nontechnical terms We believe that you cannot reject the null hypothesis that states that the average coke has more than 19.8 oz in each bottle.

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