Reference no: EM132852984

For all questions do the following:

a) Write the claim mathematically and identify the claim

b) Find the critical values and identify the rejection regions (or state the P-value)

c) Find the standardized test statistic

d) Decide whether to reject or fail to reject the null hypothesis

e) Interpret the decision in the context of the original claim

1. In your work for a national health organization, you are asked to monitor the amount of sodium in a certain brand of cereal. You find that a random sample of 52 cereal servings has a mean sodium content of 232 milligrams with a standard deviation of 10 milligrams. With a level of significance of 0.04, can you conclude that the mean sodium content per serving of cereal is less than 230 milligrams?

2. A government association claims that of 44% of adults in the U.S. do volunteer work. You work for a volunteer organization and are asked to test this claim. You find that in a random sample of 1,165 adults, 556 do volunteer work. At a significance level of 0.05, do you have enough evidence to reject the association's claim?

3. A nutritionist claims that the mean tuna consumption by a person in the United States is 3.4 pounds per year. A sample of 60 people in the United States shows that the mean tuna consumption by a person is 3.2 pounds per year with a standard deviation of 1.13 pounds. With a significance level of 0.08, can you reject the nutritionist's claim?

4. An insurance agent says that standard deviation of the total charge for patients involved in a crash in which the vehicle struck a wall is less than $18,000. A random sample of 28 total charges for patients involved in this type of crash has a standard deviation of $18,500. With a significance level of 0.10, can you support the agent's claim?

5. A travel agency estimates that the standard deviation of the room rates of hotels in a certain city is no more than $25. You work for a consumer advocacy group and are asked to test this claim. You find that a random sample of 13 hotels has a standard deviation of $27.50. With a significance level of 0.01, do you have enough evidence to reject the agency's claim?

6. An environmentalist estimates that the mean waste recycled by adults in the United States is 3 pounds per person per day. You want to test this claim. You find that the mean waste recycled per person per day for a random sample of 15 adults in the United States is 2.7 pounds and the standard deviation is 0.2 pound. With a significance level of 0.05, can you support the claim?

7. You are employed by an environmental conservation agency that recently claimed more than 42% of U.S. consumers have stopped buying a certain product because the manufacturing of the product pollutes the environment. You want to test the claim. To do so, you randomly select 2,140 U.S. consumers and find that 45% have stopped buying this product because of pollution concerns. At a significance level of 0.03, can you support the claim?

8. An organization believes that the proportion of U.S. adults who use nonprescription pain relievers is 73%.

a. Explain when a type 1 error occurs for a hypothesis test of the claim

b. Explain when a type 2 error occurs for a hypothesis test of the claim