MATH 221 Week 6 Discussion

MATH 221 Week 6 Discussion | Devry University

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. Answer the following questions:

What would the null and alternate hypotheses be? Which one would be the claim?

What kind of test is this, left tailed, right tailed or two tailed? How do you know?

Here is the information about the test statistic and p-values taken from the week 6 Excel spreadsheet.

Test Statistic and p-values           

                SE           1.060000

                Test statistic       -2.830189

                Left-sided p-value           0.002326

                Right-sided p-value         0.997674

                Two-Sided p-value          0.004652

Which p-value would you choose to use to compare the level of significance?

At α = 0.01, is there enough evidence to support the report’s claim? (Source: Association of American Medical Colleges) 

2.            How do you know when a hypothesis test is left-tailed, right-tailed or two-tailed? How is this related to the alternative hypothesis? 

3.            n this class we focus on using the p-value to validate a claim using a hypothesis test. This is not the only method. Research the method of critical regions to validate a claim using a hypothesis test.  What is it? How does it work?  Why would you use instead of, or in addition to the p-value method?

4. Shall We z or T?

4.            What are the circumstances under which we use the z-distribution for a hypothesis test? How are they different from those required to use the t-distribution? What role does the central limit theorem play?

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. Answer the following questions:

         What are the null and alternate hypothesis? How do you know? Which one is the claim, why?

         Is this a left-tailed, right tailed, or two-tailed test? How do you know?

6. Caffeine Content (continued)

6.            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. Answer the following questions:

          What is the test statistic? Is it a z or t value? Why?

         What is the P-Value? How do you know?

         If the level of significance is 0.05, will we reject or fail to reject the null hypothesis? Why?

        What conclusion can we draw about the claim?

7.            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. Answer these questions:

         Will we use the z-or t-distribution for this test? Why?

        What are the null and alternate hypothesis? How do you know? Which one is the claim, why?

        Is this a left-tailed, right tailed, or two-tailed test? How do you know? 

8.            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? Answer these questions:

          What is the P-Value? How do you know?

          If the level of significance is 0.05, will we reject or fail to reject the null hypothesis? Why?

          What conclusion can we draw about the claim? 

9.            What is the difference between a confidence interval and a hypothesis test? How can you decide which one to use to achieve a useful result? Which would you use if you wanted to find out if cars were regularly exceeding the speed limit posted near a school? Why? Which one would you use if you wanted to know if the price being asked for a used Ford Mustang is reasonable or what one should expect to be paying for a Ford Mustang? Why? 

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?