Buy three small packages of M&Ms and 5 small packages of another brand of candy (same net weight as the M&Ms). Test whether or not the mean number of candy pieces per package is the same for the two brands.
Well, this is a project you have to do... I can't do it for you, sorry.
You need data before you can do the analysis.
To test whether the mean number of candy pieces per package is the same for two different brands of candy, you will need to perform a statistical hypothesis test. Here's a step-by-step guide to help you conduct the test:
1. Purchase the necessary items: Buy three small packages of M&Ms and five small packages of the other brand of candy. Make sure the net weight of the candy packages you choose are the same as the M&Ms packages.
2. Collect the data: Open each package of candy, count the number of candy pieces in each package, and record the data. Be sure to separate the data for M&Ms and the other brand of candy.
3. Formulate the null and alternative hypotheses: The null hypothesis (H0) assumes that there is no difference between the mean number of candy pieces per package for the two brands. The alternative hypothesis (Ha) assumes that there is a difference. So, for this test, your hypotheses would be:
- H0: The mean number of candy pieces per package is the same for both brands.
- Ha: The mean number of candy pieces per package is different for the two brands.
4. Determine the appropriate statistical test: Since you are comparing the means of two independent groups (number of candy pieces in M&Ms vs. number of candy pieces in the other brand), a two-sample t-test is suitable.
5. Calculate the test statistic: Use a statistical software or a calculator to perform the two-sample t-test. You will need the sample means, sample standard deviations, and sample sizes for both groups to calculate the test statistic.
6. Determine the critical value: Determine the critical value based on your desired level of significance (e.g., alpha = 0.05). You will compare the test statistic to this critical value to draw conclusions.
7. Make a decision: Compare the test statistic to the critical value. If the test statistic falls within the rejection region (beyond the critical value), reject the null hypothesis. Conversely, if the test statistic falls within the non-rejection region (within the critical value), fail to reject the null hypothesis.
8. Interpret the results: If you reject the null hypothesis, it means there is evidence to suggest that there is a significant difference in the mean number of candy pieces per package between the two brands. If you fail to reject the null hypothesis, it means there is insufficient evidence to conclude that the means are different.
Remember, the validity of the test results depends on the data being collected and analyzed properly, so ensure accurate counts and measurements throughout the process.