4.5 Data Analytics for the Business of Life 4.5 Single Mean t Test- Exercise (re

Question

4.5 Data Analytics for the Business of Life 4.5 Single Mean t Test- Exercise (read Hawkes 11.1-11.5) . A state inspector is conducting a study to determine if a water bottling company is filling 2- iter bottles with less than 2-liters. A random sample of twenty-five bottles is selected from current production. The sample yields a mean of 1.99 liters and standard deviation of 0.025 liters. Conduct a test of hypothesis at the 0.05 significance level to determine if the sample evidence is sufficient to conclude the water bottle company is under-filling 2-liter bottles. Show all steps carefully and completely-with proper notation. Include with your decision rule a graphical rendition of the rule. Four Step Hypothesis Test Procedure 1. Hypotheses (formulate the null and alternative hypotheses) Ha: Test Statisties (specify the test statistic, and sampling distribution under Ho) 2. 3. Decision Rule (specify and decision rule) 4. Decision (compute test statistic, apply decision rule, report result) Apply the decision rule to the computed test statistic and report the result with both a technical statement and a client friendly report statement. Report detailed computations here or in a report appendix. P-vale 00810

Explanation / Answer

Answee to the question is as follows:

1. Ho: Mu <=2
Ha: Mu > 2

2. this is t-distribution. sampling distribution is a t-distribution
test statistic = (xbar - Mu)/(s/sqrt(n)) = (1.99-2)/(.025/sqrt(25)) = -2

3. alpha = .05, decision rule, if p-value < alpha , then reject Ho

4. the p-value is P(t<-2) = ?
At df = n-1=24, alpha = .05, we have t critical = -1.711
Since, -2 is less than -1.711 we reject Ho
Result: We reject null hypothesis and conclude that the water bottling company is filling 2l bottles with less
than 2 liters

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