# 10.6: Hypothesis Testing for Two Means and Two Proportions (Worksheet)

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- 4951

- Contributed by Barbara Illowsky & Susan Dean
- Statistics at De Anza College
- Sourced from OpenStax

Name: ______________________________

Section: _____________________________

Student ID#:__________________________

*Work in groups on these problems. You should try to answer the questions without referring to your textbook. If you get stuck, try asking another group for help.*

**Student Learning Outcomes**

- The student will select the appropriate distributions to use in each case.
- The student will conduct hypothesis tests and interpret the results.

**Supplies:**

- the business section from two consecutive days’ newspapers
- three small packages of M&Ms®
- five small packages of Reese's Pieces®

**Increasing Stocks Survey**

- \(H_{0}\):
*_________* - \(H_{a}\)
*: _________* - In words, define the random variable.
- The distribution to use for the test is _____________.
- Calculate the test statistic using your data.
- Draw a graph and label it appropriately. Shade the actual level of significance.
- Graph:
**Figure 10.6.1.** - Calculate the \(p\text{-value}\).

- Graph:
- Do you reject or not reject the null hypothesis? Why?
- Write a clear conclusion using a complete sentence.

**Decreasing Stocks Survey**

- \(H_{0}\): ________
- \(H_{a}\)
*: ________* - In words, define the random variable.
- The distribution to use for the test is _____________.
- Calculate the test statistic using your data.
- Draw a graph and label it appropriately. Shade the actual level of significance.
- Graph:
**Figure 10.6.2.** - Calculate the \(p\text{-value}\):

- Graph:
- Do you reject or not reject the null hypothesis? Why?
- Write a clear conclusion using a complete sentence.

**Candy Survey**

Buy three small packages of M&Ms and five small packages of Reese's Pieces (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.

- \(H_{0}\): ________
- \(H_{a}\): ________
- In words, define the random variable.
- What distribution should be used for this test?
- Calculate the test statistic using your data.
- Draw a graph and label it appropriately. Shade the actual level of significance.
- Graph:
**Figure 10.6.3.** - Calculate the \(p\text{-value}\).

- Graph:
- Do you reject or not reject the null hypothesis? Why?
- Write a clear conclusion using a complete sentence.

**Shoe Survey**

Test whether women have, on average, more pairs of shoes than men. Include all forms of sneakers, shoes, sandals, and boots. Use your class as the sample.

- \(H_{0}\): ________
- \(H_{a}\): ________
- In words, define the random variable.
- The distribution to use for the test is ________________.
- Calculate the test statistic using your data.
- Draw a graph and label it appropriately. Shade the actual level of significance.
- Graph:
**Figure 10.6.4.** - Calculate the \(p\text{-value}\).

- Graph:
- Do you reject or not reject the null hypothesis? Why?
- Write a clear conclusion using a complete sentence.