Hypothesis Test on Cookie Chips

Hypothesis Test on 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?

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 on Cookie Chips

1. What parameters are being compared?,

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

3. What populations do the cookie samples represent?,

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

5. Are the samples random and independent?

Comprehensive General Answer:

1. Parameters Being Compared:

The participants are comparing the mean number of chocolate chips per cookie for two different brands:

• Chips Amor cookies

• Local grocery store brand cookies

So, the parameter being compared is the mean number of chocolate chips per cookie for each brand.

2. Null and Alternative Hypotheses:

To statistically test the claim that Chips Amor cookies have more chocolate chips, we define:

• Null Hypothesis (H₀):
  There is no difference in the mean number of chocolate chips between Chips Amor cookies and the grocery store brand.
  H0:μA≤μBH_0: mu_A leq mu_BH0​:μA​≤μB​

• Alternative (Research) Hypothesis (H₁):
  Chips Amor cookies have more chocolate chips on average than the grocery store brand.
  H1:μA>μBH_1: mu_A > mu_BH1​:μA​>μB​

Hypothesis Test on Cookie Chips

3. Populations from Which the Samples Came:

• Population A: All Chips Amor cookies

• Population B: All cookies made by the local grocery store brand

The 30 participants each received one cookie from each brand. Each cookie they received represents a sample from each population.

4. One-Tailed or Two-Tailed Test?

This is a one-tailed test, because the alternative hypothesis specifies a direction — that Chips Amor cookies have more chips than the other brand.

5. Are the Samples Random and Independent?

• Random Samples:
  If the cookies were randomly selected from a large batch of each brand, then yes — the samples can be considered random. If not, there may be selection bias.

• Independent Samples:
  No — the samples are not independent, because each participant compares both cookies (one from each brand). This makes it a paired sample design, meaning the observations are dependent (matched pairs).

• Hypothesis Test on Cookie Chips

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