Is there a significant difference in calories between...

Is there a significant difference in calories between servings of strawberry and vanilla yogurt? Based on the data shown in the table, test an appropriate hypothesis and state your conclusion. Don't forget to check assumptions and conditions! $$\begin{array}{l|c|c}\hline & {\text { Calories per Serving }} \\ \text { Brand } & \text { Strawberry } & \text { Vanilla } \\ \hline \text { America's Choice } & 210 & 200 \\ \text { Breyer's Lowfat } & 220 & 220 \\\text { Columbo } & 220 & 180 \\\text { Dannon Light'n Fit } & 120 & 120 \\\text { Dannon Lowfat } & 210 & 230 \\\text { Dannon la Crème } & 140 & 140 \\\text { Great Value } & 180 & 80 \\\text { La Yogurt } & 170 & 160 \\ \text { Mountain High } & 200 & 170 \\\text { Stonyfield Farm } & 100 & 120 \\ \text { Yoplait Custard } & 190 & 190 \\\text { Yoplait Light } & 100 & 100\end{array}$$

Is there a significant difference in calories between servings of strawberry and vanilla yogurt? Based on the data shown in the table, test an appropriate hypothesis and state your conclusion. Don't forget to check assumptions and conditions!
$$\begin{array}{l|c|c}\hline & {\text { Calories per Serving }} \\
\text { Brand } & \text { Strawberry } & \text { Vanilla } \\
\hline \text { America's Choice } & 210 & 200 \\
\text { Breyer's Lowfat } & 220 & 220 \\\text { Columbo } & 220 & 180 \\\text { Dannon Light'n Fit } & 120 & 120 \\\text { Dannon Lowfat } & 210 & 230 \\\text { Dannon la Crème } & 140 & 140 \\\text { Great Value } & 180 & 80 \\\text { La Yogurt } & 170 & 160 \\
\text { Mountain High } & 200 & 170 \\\text { Stonyfield Farm } & 100 & 120 \\
\text { Yoplait Custard } & 190 & 190 \\\text { Yoplait Light } & 100 & 100\end{array}$$

Key Concepts

Statistical Hypothesis Testing

This concept involves formulating a null hypothesis (typically stating that there is no difference between groups) and an alternative hypothesis (indicating some difference exists), and then using sample data to determine whether there is strong evidence to reject the null hypothesis. It is a fundamental approach in statistics for making inferences about populations based on samples.

Paired Sample Design

A paired sample design is used when observations in two groups are not independent but are somehow related or matched. For example, measurements taken from the same subjects under two different conditions allow one to analyze the differences within pairs, which helps in reducing variability and increasing the test’s sensitivity.

Paired t-Test

The paired t-test is a statistical procedure specifically designed for comparing the means of two related groups. It examines the differences within pairs of observations to determine if the average difference is statistically significantly different from zero, making it appropriate when each subject or unit is measured twice under different conditions.

Assumptions and Conditions

When conducting a paired t-test, it is important to check several assumptions: (1) The differences between paired observations should be approximately normally distributed, which can be assessed using visual methods (like Q-Q plots) or statistical tests; (2) The sample of differences should be independent; and (3) The paired design itself assumes that the pairing was done appropriately such that variability due to other factors is controlled.

Transcript

00:01 All right, in this problem, we're given a table with a bunch of brands of yogurt and their brands that have strawberry and vanilla flavor.

00:10 So for each brand, the calories in the strawberry yogurt is recorded in this column, and then the calories for the vanilla yogurt is recorded in the next column.

00:21 We want to know is there a significant difference in calories between strawberry and vanilla yogurt? and we want to check our conditions for inference and make sure those are good to go.

00:33 Let's start with which type of test we should do.

00:36 Do we want a paired tea test or a two sample tea test? if it was going to be two samples, strawberry and vanilla calorie amounts would need to be very independent of each other.

00:45 But because for one brand, you're getting both amounts, both calories, we cannot say that these are independent.

00:52 These are paired together naturally.

00:54 That could be because certain brands have ingredients or special recipes they use to make their yogurt, and so that recipe is going to affect both the strawberry calories and the vanilla calories.

01:06 So we want to pair those together.

01:08 Therefore, we are going to be using a paired tea test.

01:15 T test.

01:18 Before we get started, let's check our conditions.

01:21 Pared, we just talked about.

01:23 It's got to be paired because each brand has two pieces of data, one in each column.

01:28 We got to pair them together.

01:29 Second, is it independent? one company's recipe and amount of calories should be independent from another companies.

01:38 But what they do should not affect the other companies.

01:41 So we're just going to give it a green check mark because we're good to go.

01:44 Random.

01:47 Hopefully the companies were chosen at random.

01:49 It wasn't just like a bunch of companies from one part of the country maybe and ignoring all the other states.

01:55 That would definitely skew our data or could.

01:58 This was hopefully just a random sample from all around the nation or wherever we're going to be generalizing too.

02:03 So if it's worldwide, we want to get some from all over the world.

02:06 If it's just in the u .s., we just want some from the u .s., right? so we're going to assume they did that because hopefully they're good statisticians.

02:14 And then we need to test the 10 % rule if we're going to generalize.

02:21 10 % rule means that we need to test only up to 10 % of brands.

02:29 I believe, let's be a me check my list, but i believe we had 12 brands.

02:40 Yes, we had 12 brands.

02:42 So that means there need to be at least 120 brands that we're generalizing to.

02:51 So let's just assume there are going to be 120 brands.

02:53 That's a lot of brands, but you never know.

02:55 And then let's check our nearly normal rule.

03:02 Nearly normal.

03:03 All right, to test nearly normal.

03:04 We're going to need to already get our third list going in a paired tea test.

03:08 Remember, we are testing the difference between list one and list two.