In selecting a test statistic for a hypothesis test, a given sample has to satisfy some conditions. The first is based on the nature of the sample concerning whether it follows a normal distribution or not. In using the z or t- statistic, an assumption must be made that the data follows a standard normal distribution. The other consideration is the sample size, which determines the selection of a test statistic. In regard to samples that are greater than thirty, the test statistic that is used is the z-statistic; whereas, for samples that are less than thirty, the t-statistic is utilized. In addition, the population’s standard deviation should be determinable. Thus, despite the population of Team C is unknown, it is normally distributed, however, given its sample size n = 30, the sample Standard deviation can be determined and can be used to calculate its statistic. Thus, on this basis, Team C will choose the Z-statistic as their test statistic.
The specific conditions under which the H0 is rejected and the conditions under which it is not rejected is known as a decision rule. The region of H0 rejection represents the location of all z values that are significantly large or small to the point that the chances of occurrence under null hypothesis are not likely. Upon Team C utilizing a two-tailed test means that the focus is not on the size of the sample in reference to the proposed population mean, but instead, in whether mean is different from the proposed value for the population means of $3.330 a gallon. This is based on the population and the assumption that the sample’s standard deviation is 0.18580.
The decision rule is derived by finding the critical values of z. Using a two-tailed test, 1/2(0.05)= 0.025, i.e. 0.025 is placed in each tail. The region where H0 is not rejected is located between the two tails, is therefore 0.95. This is based on half of the area under the curve, or 0.5000.
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