Mean is the average that is obtained by summing up all the numbers and dividing by the number of observations (Curwin & Slater, 2008). The median is the middle value when data in a data set is order either in ascending or descending order (Curwin & Slater, 2008). Mean and Median are measures of central tendency, as they measure how values scatter around a central value (Lucey, 2002). The standard deviation is a measure of dispersion that measures how much individual values deviate from the mean (Lucey, 2002).
The bottles sampled were found to contain on average 15.854 ounces with a standard deviation of 0.6614 ounces. The sampled bottles had a median content of 15.99 ounces. Since the mean and median content are below the recommended amount of 16 ounces. It is necessary to carry out a hypothesis tests in order to determine whether the customer complaints that the bottles contain less than the advertised sixteen ounces are valid.
A hypothesis test is a scientific way of testing whether a claim is true or false by using statistical means (Lucey, 2002).The hypothesis test involves the following steps:
Step 1: Set the null hypothesis, the null hypothesis is the claim that is to be tested and is denoted as Ho. In this case, the null hypothesis is set as follows:
Ho: µ=16.00
The hypothesis assumes that the sample mean is equivalent to the recommended content of 16.0 ounces.
Step 2: after setting the null hypothesis it is important to set the alternative hypothesis that a researcher will adopt incase the null hypothesis is rejected (Buglear, 2001). The alternative hypothesis is denoted as H1. In this case, the alternative hypothesis is set as follows:
H1: µ≠16.00
The alternative hypothesis assumes that the sample mean is not equal to the hypothetical mean content of 16.00 ounces.
Step 3: Determine the level of significance and the Z critical. In this case, the level of significance is given as 5%. Since it’s a two tail test, the Z critical = 1.96
When a researcher fails to reject the null hypothesis, it indicates either that the null hypothesis is true or that there is no sufficient evidence to reject the null hypothesis. The significance level measures the probability that a researcher will reject a true hypothesis. In this case, there is a 5% chance that the researcher will conclude that there is no significant difference between the hypothetical mean and the sample mean when in reality the two means are significantly different (Lucey, 2002).
Step 4: calculate the Z statistic. The Z statistic is calculated as follows:
Z = (X - µ)/∂
Z = (15.854 – 16.00)/0.6614 = -0.22
Step5: This involves comparing the Z statistic to the Z critical. If the Z statistic is less than the Z critical, accept the null hypothesis and conclude that there is no significant difference between the sample mean and the hypothetical mean at the given level of significance (Lucey, 2002). On the other hand, if the Z statistic is greater than the Z critical, reject the null hypothesis and conclude that there is a significant difference between the hypothetical mean and the sample mean at the given level of significance (Lucey, 2002). In this case since the Z statistic of -0.22 is less than the Z critical of 1.96, we accept the null hypothesis and conclude that there is no significant difference between the sample mean of 15.854 ounces and the hypothetical mean of 16.0 ounces. Therefore, the customers claim that the bottles content are less than the advertised Sixteen ounces is not justified.
Reference list
Buglear, J. (2001). Stats means business: A guide to business statistics. Oxford: Buttworth-
Heinemann.
Curwin, J., & Slater, R. (2008). Quantitative methods for business decisions. London: South-
Western Cengage Learning.
Lucey, T. (2002). Quantitative techniques. London: Thomson.
