Hypotheses in the Real World

Hypotheses in the Real World

(Required) Create and post a response that fully answers one of the 10 questions below (no later than Wednesday)

(Required) Create and post a response that fully answers a different one of the 10 questions below (on a different day)

(Required) Post one quality response to another classmates’ “main” post or to a professor post (by the end of the week).

(Required) The posts must be submitted on at least 3 different days.

(Optional) Additional posts and/or days of participation are not required, but are certainly welcome!

NOTE: Always paste the question itself (and its number) above your answer (or enough of it, when it’s a really long question, to make it clear which one you are addressing).

Special Instructions for Questions 1-9:

Select a problem below.  For your first post, complete the following steps:

a. identify the claim and state H0 and Ha.

b. find the standardized test statistic z or t OR find the corresponding P-value.

c. Identify the type of test. Compare the p-value with α OR the standardized test statistic with the critical value of z or t

For your second post, reply to another student’s first post and complete the problem with these steps:

d. decide whether to reject or fail to reject the null hypothesis. based on the test statistic or the p-value

e. interpret the decision in the context of the original claim.

For your subsequent posts, consider another way to look at the problem, respectfully propose a different structure or response, or use the same problem changing one element (e.g., number in sample, standard deviation, or claim) to post it again.

For full posting guidelines, review the Real World Discussions: Requirements page.

1. A Random Sample of…

1. A random sample of 100 medical school applicants at a university has a mean total score of 502 on the MCAT. According to a report, the mean total score for the school’s applicants is more than 499. Assume the population standard deviation is 10.6. At α = 0.01, is there enough evidence to support the report’s claim? (Source: Association of American Medical Colleges)

2. Sprinkler Systems

2. Sprinkler Systems: A manufacturer of sprinkler systems designed for fire protection claims that the average activating temperature is at least 135°F. To test this claim, you randomly select a sample of 32 systems and find the mean activation temperature to be 133°F. Assume the population standard deviation is 3.3°F. At α = 0.10, do you have enough evidence to reject the manufacturer’s claim?

3. Boston Marathon

3. Boston Marathon: A sports statistician claims that the mean winning times for Boston Marathon women’s open division champions is at least 2.68 hours. The mean winning time of a sample of 30 randomly selected Boston Marathon women’s open division champions is 2.60 hours. Assume the population standard deviation is 0.32 hour. At α = 0.05, can you reject the claim? (Source: Boston Athletic Association)

4. A Consumer Group Claims…

4. A consumer group claims that the mean acceleration time from 0 to 60 miles per hour for a sedan is 6.3 seconds. A random sample of 33 sedans has a mean acceleration time from 0 to 60 miles per hour of 7.2 seconds. Assume the population standard deviation is 2.5 seconds. At α = 0.05, can you reject the claim? (Source: Zero to 60 Times)

5. Caffeine Content

5. Caffeine Content: A consumer research organization states that the mean caffeine content per 12-ounce bottle of a population of caffeinated soft drinks is 37.7 milligrams. You want to test this claim. During your tests, you find that a random sample of thirty-six 12-ounce bottles of caffeinated soft drinks has a mean caffeine content of 36.4 milligrams. Assume the population standard deviation is 10.8 milligrams. At α = 0.01, can you reject the research organization’s claim? (Source: National Soft Drink Association)

6. Fast Food

6. Fast Food: A fast-food restaurant estimates that the mean sodium content in one of its breakfast sandwiches is no more than 920 milligrams. A random sample of 44 breakfast sandwiches has a mean sodium content of 925 milligrams. Assume the population standard deviation is 18 milligrams. At α = 0.10, do you have enough evidence to reject the restaurant’s claim?

7. Light Bulbs

7. Light Bulbs: A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least 750 hours. A random sample of 25 light bulbs has a mean life of 745 hours. Assume the population is normally distributed and the population standard deviation is 60 hours. At α = 0.02, do you have enough evidence to reject the manufacturer’s claim?

8. Used Car Cost8. Used Car Cost: A used car dealer says that the mean price of a three-year-old sport utility vehicle (in good condition) is $20,000. You suspect this claim is incorrect and find that a random sample of 22 similar vehicles has a mean price of $20,640 and a standard deviation of $1990. Is there enough evidence to reject the claim at α = 0.05?

9. DMV Wait Times

9. DMV Wait Times: A state department of Transportation claims that the mean wait time for various services at its different locations is at most 6 minutes. A random sample of 34 services at different locations has a mean wait time of 10.3 minutes and a standard deviation of 8.0 minutes. Is there enough evidence to reject the claim at α = 0.01?

10. Ethics! (How it’s stated?)

10. Ethics:  Which hypothesis, the null or the alternative, is easiest for the math to support?  Knowing that, could someone state their hypothesis so that it is the most likely to be supported?  Should every hypothesis test be done with various wordings of the claim, or is there a structure to the hypotheses that should be followed?

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