10.5 Hypothesis Testing for Two Means and Two Proportions

Hypothesis Testing for Two Means and Two Proportions

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.

Increasing Stocks Survey
Look at yesterday’s newspaper business section. Conduct a hypothesis test to determine if the proportion of New York Stock Exchange (NYSE) stocks that increased is greater than the proportion of NASDAQ stocks that increased. As randomly as possible, choose 40 NYSE stocks and 32 NASDAQ stocks and complete the following statements.

1. H₀: _________
2. H_a: _________
3. In words, define the random variable.
4. The distribution to use for the test is _____________.
5. Calculate the test statistic using your data.
6. Draw a graph and label it appropriately. Shade the actual level of significance.
   1. Graph:

      Figure 10.13
   2. Calculate the p value.
7. Do you reject or not reject the null hypothesis? Why?
8. Write a clear conclusion using a complete sentence.

Decreasing Stocks SurveyRandomly pick eight stocks from the newspaper. Using two consecutive days’ business sections, test whether the stocks went down, on average, for the second day.

1. H₀: ________
2. H_a: ________
3. In words, define the random variable.
4. The distribution to use for the test is _____________.
5. Calculate the test statistic using your data.
6. Draw a graph and label it appropriately. Shade the actual level of significance.
   1. Graph

      Figure 10.14
   2. Calculate the p value:
7. Do you reject or not reject the null hypothesis? Why?
8. Write a clear conclusion using a complete sentence.

Candy SurveyBuy three small packages of multicolored chocolates and five small packages of peanut butter candies (same net weight as the multicolored chocolates). Test whether the mean number of candy pieces per package is the same for the two brands.

1. H₀: ________
2. H_a: ________
3. In words, define the random variable.
4. What distribution should be used for this test?
5. Calculate the test statistic using your data.
6. Draw a graph and label it appropriately. Shade the actual level of significance.
   1. Graph

      Figure 10.15
   2. Calculate the p value.
7. Do you reject or not reject the null hypothesis? Why?
8. 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.

1. H₀: ________
2. H_a: ________
3. In words, define the random variable.
4. The distribution to use for the test is ________________.
5. Calculate the test statistic using your data.
6. Draw a graph and label it appropriately. Shade the actual level of significance.
   1. Graph

      Figure 10.16
   2. Calculate the p value.
7. Do you reject or not reject the null hypothesis? Why?
8. Write a clear conclusion using a complete sentence.