In the following table there are the following variables 1 C

In the following table, there are the following variables:

1) Cereal Type (Regular or Healthy Alternative). Please note: In the Excel spreadsheet, Regular is coded with the number \"1\" and Healthy Alternative is coded with the number \"2\"

2) Calories: See the below graph!!!!

Please complete and answer the following three things:

1. What statistical technique should be used to analyze the data? Why? What is the explanatory/independent variable? What is the response/dependent variable?

2. Calculate the descriptive statistics for each group. Specifically, calculate the mean, standard deviation, and sample size (n) for the two groups: 1) regular cereal and 2) healthy alternative cereal: thus, you should end up with a sample mean for calories for the healthy alternative cereal and a sample mean for calories for regular cereal. These numbers can be calculated by hand or with software. Put the numbers in the following table. Note: these are the numbers that will be needed to plug into the t-test statistic formula.

3. Perform all four steps of the appropriate hypothesis test on the data.

Step 1: Stating the Hypotheses

Step 2: Check Conditions, and Summarize the Data Using a Test Statistic

Please hand calculate the t-test statistic using the numbers derived from #2 above and the formula in OLI.

Step 3: Finding the p-value of the test

Since the p-value would need to be calculated with statistical software, I am giving you the p-value. After running the correct statistical technique, the p-value is: .088

Step 4: Conclusion in context

What do the results show about the null hypothesis? What does it mean in real life terms (ex. Is there a difference in calories?).

11-10-11-11-11-11-13 11 11 20 20 | 2 20 at 11-12 1

Solution

1. The statistical technique to be used is the Students T-test (Hypothsis testing). The 2nd application of t-test allows us to analyze whether there is a significant difference between the means of 2 samples from different populations.

In the given case, both the variables are independent.

2. For Regular Cereal - Mean = 116, S.D. = 5.87 & n = 10

For Healthy Alternative - Mean = 148.5, S.D. = 56.65 & n = 10

3. The Hypothesis Test

H₀: Mean of Regular Cereal = Mean of Healthy Alternative

H₁: Mean of Regular Cereal is not equal to the Mean of Healthy Alternative

Thus, it is a 2 tailed test.

Calculation of t-test statistic

t-test statistic = difference between the means / pooled standard deviation

[pooled standard deviation = square root of the weighted average of the variances]

t-test statistic = (148.5 - 116) / 40.27

t-test statistic = 0.807

3. p-value = 0.087924

4. Conclusion: With 91.2% (1-0.088) confidence, we can say that there is a significant difference between the mean calories of a regular cereal and a healthy alternative.