Hypothesis Test – Cookie Chips

Hypothesis Test – Cookie Chips

Imagine you are a product manager at Chips Amor Cookie Company and you want to test how accurate the claim is that your cookies have more chocolate chips than the those produced by a local grocery store brand.

To do this, you gather a team of consumers to compare the cookies. You give each participant a Chips Amor cookie in a bag labeled A and a local grocery store brand cookie in a bag labeled B. They are asked to count the number chips in each cookie. You have 30 participants.

• What parameters would they be comparing?,
• How can you write a null hypothesis and an alternative hypothesis?,
• What are the populations from which the samples came?,
• Based on your hypothesis is this a one-tailed or two-tailed test?
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Write a null hypothesis and a research hypothesis:

• So, are the samples of cookies random?
• Are the two samples independent of each other?

Hypothesis Test – Cookie Chips

1. What parameters would participants be comparing?

2. How can you write a null and alternative hypothesis?

3. What are the populations from which the samples came?

4. Is this a one-tailed or two-tailed test?

5. Are the samples random and independent?

Comprehensive General Answer

This scenario involves a comparison of two different cookie brands—Chips Amor and a local grocery store brand—to determine if there is a statistically significant difference in the number of chocolate chips per cookie.

1. Parameters Being Compared

The participants are comparing the mean number of chocolate chips in the two types of cookies. So the parameter of interest is the average number of chips per cookie for each brand.

2. Null and Alternative Hypotheses

These hypotheses are written to test the claim that Chips Amor has more chocolate chips than the local brand.

• Null Hypothesis (H₀): There is no difference or the Chips Amor cookies do not have more chips than the local brand.
  H0:μA≤μBH₀: \mu_A \leq \mu_BH0​:μA​≤μB​

• Alternative Hypothesis (H₁): Chips Amor cookies have more chocolate chips than the local brand.
  H1:μA>μBH₁: \mu_A > \mu_BH1​:μA​>μB​

Where:

• μA\mu_AμA​ = mean number of chips in Chips Amor cookies

• μB\mu_BμB​ = mean number of chips in the local grocery brand

3. Populations of Interest

• Population 1: All Chips Amor cookies

• Population 2: All cookies from the local grocery store brand

The samples taken from each cookie type aim to represent these two larger populations.

4. One-Tailed or Two-Tailed Test?

This is a one-tailed test because the hypothesis specifically tests whether Chips Amor has more chips—not simply a difference in either direction.

Hypothesis Test – Cookie Chips

5. Sample Randomness and Independence

• Random Samples?
  Not entirely. The participants did not randomly select cookies from the entire population; they were provided with specific cookies. This could introduce selection bias, so it is not a fully random sample.

• Independent Samples?
  Yes. Each participant receives one cookie from each brand, and their chip counts are for two different products. Even though the same participants are comparing both cookies, the cookies themselves come from two independent sources, making the samples independent of each other.

Note: If each participant’s comparison is paired (e.g., they rate both cookies), a paired t-test may also be appropriate, depending on the data collection method.