The week 5 assignment addressed point and confidence interval estimation, one of the two major divisions of inferential statistics. The remaining weeks of this course bring together everything we've covered in this course thus far in our study of the second division of inferential statistics: hypothesis tests. The Week 6 written assignment requires that you select and conduct the most appropriate goodness-of-fit hypothesis test. Here are a few pointers to assist you:
The goodness-of-fit hypothesis tests are listed and described in section 4.2 of the textbook. To determine the best test to use for this assignment, examine the purpose of each of these tests and compare it to what you need to do for the week 6 assignment.
- the one-sample t-test is used to compare a calculated sample mean of a continuous variable (interval or ratio scale) to some hypothesized value to determine if there is a difference.
- the Kolmogorov-Smirnov test is used to compare a given distribution of a continuous variable (interval or ratio scale) to a normal distribution to determine if there is a difference in the shape of the distribution.
- the chi-square goodness-of-fit test is used to compare the observed frequencies of a categorical variable (nominal scale) to expected frequencies.
Look at the scale of measurement of your dependent variable (sugar grams). Each of the goodness-of-fit tests has specific requirements. For example, the one-sample t-test and the Kolmogorov-Smirnov test require that the scale of measurement of the dependent variable (DV) is interval or ratio scale while the chi-square goodness-of-fit test requires that the DV is a categorical variable (i.e., nominal scale).
2. The best measures of central tendency and dispersion to report in cells A35:B36 depend on the DV's scale of measurement.
- Ratio and interval scale variables: report means and standard deviation.
- Ordinal scale variables: report median and range.
- Nominal scale variables: report mode and range.
3. The test value that you are required to place in cell B37 is identified in the null hypothesis. It is the value to which you compare the sample mean.
4. The appropriate test statistic that you are to enter in cell B38 depends on the hypothesis test you conduct. For example, the one-sample t-test uses the t-statistic and the chi-square goodness-of-fit test uses the chi-square statistic. Identify the statistic that you calculate in cell A38, e.g., t or chi-square.
5. You must show all your work and enter formulas! You will not receive full credit if you show the correct value for a statistic but not show the formula you used to obtain that statistic. Once you select the most appropriate hypothesis test, follow the textbook procedures, step-by-step, for this test using the sugar grams variable.
6. A reported p-value can never be zero. When reporting results using APA style, never report a p-value of zero, e.g., p = .00. (Excel rounds numbers, so if you see .00 in a calculated Excel field it may actually be something like .00034.) Instead, report the actual p-value, e.g., p = .0003, or write p < .01. A p-value of zero means there is no chance of error. There is always a chance of error with hypothesis testing, which is why we avoid stating the hypothesis test "proves" the statistical decision.
7. The assignment requires that you evaluate the null hypothesis: "There is no difference in mean grams of sugar of packaged cake mixes and the sugar content of a new cake mix that contains 13 grams of sugar." The results of your analysis will lead you to one of two statistical decisions:
- If p <= 0.05: There is sufficient evidence to reject this hypothesis (i.e., there is a statistically significant difference between the sample mean and the hypothesized test value of 13). The null hypothesis is false.
- If p > 0.05: There is insufficient evidence to reject this hypothesis (i.e., the null hypothesis is true; the difference between the sample mean and 13 is not statistically significant.) The difference between the sample mean and 13 can be explained by measurement error.
8. As always, you must show all your work by entering formulas. As usual, DO NOT use automated procedures (i.e., Analysis ToolPak or StatPlus plug-in)
9. Very closely follow the example in the textbook of what to report for your hypothesis test in a research report results section. There is an example results narrative in the textbook for each test located under the heading Reporting Test Results (you can locate this section at the end of each hypothesis test procedures). This example adheres to an APA style results narrative for your selected test. Be precise! Do not provide a simple table summary.