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MAT 130 MODULE 5 CHECK YOUR UNDERSTANDING

1.	Express the null hypothesis and the alternative hypothesis in symbolic form. Use the correct symbol ( , p,  ) for the indicated parameter. A researcher claims that the amounts of acetaminophen in a certain brand of cold tables have a standard deviation different from the   - 3.3 mg claimed by the manufacturer.

2.	Formulate the indicated conclusion in nontechnical terms. Be sure to address the original claim. The manufacturer of a refrigerator system for beer kegs produces refrigerators that are supposed to maintain a true mean temperature,  , of 45°F, ideal for a certain type of German pilsner. The owner of the brewery does not agree with the refrigerator manufacture and claims he can prove that the true mean temperature is incorrect. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms.

3.	Find the P-value for the indicated hypothesis test. In a sample of 47 adults selected randomly from one town, it is found that 9 of them have been exposed to a particular strain of the flu. Find the P-value for a test of the claim that the proportion of all adults in the town that have been exposed to this strain of the flu is 8%.

4.	Assume that you plan to use a significance level of   = 0.05 to test the claim that p1 = p2. Use the given sample sizes and numbers of successes to find the z test statistic for the hypothesis test. A random sample of sixty pitchers from the National League and fifty-two pitchers from the American League showed that 19 national and 7 American League pitchers had E.R.A's below 3.5.

5.	Use the given information to find the P-value. Also, use a 0.05 significance level and state the conclusion about the null hypothesis (reject the null hypothesis or fail to reject the null hypothesis). With H1: p > 0.267, the test statistic is z = 156.

6.	Assume that a hypothesis test of the given claim will conducted. Identify the type I or type II error for the test. A medical researcher claims that 20% of children suffer from a certain disorder. Identify the type I error for the test.

7.	Determine whether the hypothesis test involves a sampling distribution of means that is a normal distribution, Student t distribution, or neither. You may use Figure 7-6 and Table 7-1 in your textbook. Claim about IQ scores of statistics instructors:   >100. Sample data: n = 15,   = 118, s = 11. The sample data appear to come from a normally distributed population with unknown   and  .

8.	Determine whether the given conditions justify testing a claim about a population mean  . For a simple random sample, the size is n = 25,   = 5.93, and the original population is normally distributed.

9.	The effect of caffeine as an ingredient is tested with a sample of regular soda and another sample with decaffeinated soda.

10.	Assume that a hypothesis test of the given claim will be conducted. Identify the type I or type II error for the test. A skeptical paranormal researcher claims that the proportion of Americans that have seen a UFO is less than 5 in a thousand. Identify the type I error for the test.

11.	Determine whether the samples are independent or dependent if possible. To test the effectiveness of Lipitor, cholesterol levels are measured in 250 subjects before and after Lipitor treatments.

12.	Find the P-value for the indicated hypothesis test. A manufacturer claims that fewer than 6% of its fax machines are defective. In a random sample of 97 such fax machines, 5% are defective. Find the P-value for a test of the manufacturer's claim.

13.	Assume that you plan to use a significance level of   = 0.05 to test the claim that p1 = p2. Use the given sample sizes and numbers for successes to find the P-value for the hypothesis test. n1 = 200. n2 = 100. x1 = 11. x2 = 8

14.	Assume that you plan to use a significance level of   = 0.05 to test the claim that P1 = P2. Use the given sample sizes and numbers of successes to find the z test statistic for the hypothesis test. In a vote on the Clean Water bill, 44% of the 205 Democrats voted for the bill while 46% of the 230 Republicans voted for it.

15.	Find the number of successes x suggested by the given statement. A computer manufacturer randomly selects 2280 of its computers for quality assurance and finds that 2.72% of these computers are found to be defective.

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