During your spring break you decided to take a fishing trip. You caught and released two different types of bass. For each fish, you recorded its weight as in the following table. Florida Bass Weight in lbs. 6.8 7.2 12.6 10.5 7.4 13.1 11.4 6.9 6.8 12.9 Northern Bass Weight in lbs. 6.5 7.2 6.7 6.2 8.3 6.4 8.2 12.2 10.8 6.8 Assume that weights of both the Florida bass and the Northern bass are normally distributed. Use a 0.01 significance level to test the claim of a biologist that the mean weight of the Florida bass is different from the mean weight of the Northern bass. Use the following steps: Step 1. Write the Claim, Null Hypothesis and Alternative Hypothesis in symbols. Step 2. Identify Step 3. Check and identify the requirements for this test. Step 4. State the test statistic and P-value (use Excel but do not round the results) Step 5. State your decision to either reject or fail to reject the null hypothesis and why. Step 6. Consider the claim and your decision and state the conclusion in the context of the problem.
Problem 1.
During your spring break you decided to take a fishing trip. You caught and released two different types of bass. For each fish, you recorded its weight as in the following table.
|
Florida Bass Weight in lbs. |
6.8 |
7.2 |
12.6 |
10.5 |
7.4 |
13.1 |
11.4 |
6.9 |
6.8 |
12.9 |
|
Northern Bass Weight in lbs. |
6.5 |
7.2 |
6.7 |
6.2 |
8.3 |
6.4 |
8.2 |
12.2 |
10.8 |
6.8 |
Assume that weights of both the Florida bass and the Northern bass are
Use the following steps:
Step 1. Write the Claim, Null Hypothesis and Alternative Hypothesis in symbols.
Step 2. Identify
Step 3. Check and identify the requirements for this test.
Step 4. State the test statistic and P-value (use Excel but do not round the results)
Step 5. State your decision to either reject or fail to reject the null hypothesis and why.
Step 6. Consider the claim and your decision and state the conclusion in the context of the problem.
Problem 2. COURSE LEARNING OUTCOME
Perform a hypothesis test for two population proportions. Give the null hypothesis, alternative hypothesis, reject or fail to reject the null hypothesis, and give the conclusion.
- For the Claim state the null hypothesis and alternative hypothesis in symbols
- For the P-value = 0.073, state whether you reject or fail to reject the null hypothesis if the significance level is 0.05 and why.
- State the conclusion of the problem.
Problem 3. ECHINACEA TO PREVENT COMMON COLDS
Rhinovirus typically cause common colds. In a study to prevent common colds, subjects are divided into two groups. In group #1, 45 subjects were treated with echinacea and 38 of them developed rhinovirus infections. In group #2, 103 subjects were given a placebo and 88 of them developed rhinovirus infections. Use a 0.05 significance level to test the claim that people taking echinacea develop less rhinovirus infections than people who do not take echinacea.
Use the following steps:
Step 1. Write the Claim, Null Hypothesis and Alternative Hypothesis in symbols.
Step 2. Identify
Step 3. Check and identify the requirements for this test.
Step 4. State the type of test (right-tail, left-tail, or two-tail test) and use the given test statistic to find the P-value (use the provided Standard Normal Distribution table, aka z-table, without rounding)
Test statistic
Step 5. State your decision to either reject or fail to reject the null hypothesis and why.
Step 6. Consider the claim and your decision and state the conclusion in the context of the problem.
Step 7. Considering your conclusion from part 6, does echinacea seem to be effective in preventing the common colds? Why or why not?
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