The article Helmet Heads ( Reuters, 7/3/2000) reports on one Georgia community's efforts to increase use of bicycle helmets. A study, published in the July issue of Pediatrics, said that in the U. S. only about one child in four wears a helmet while biking, despite evidence that bicycle-related head injuries cause 150 deaths and 45,000 other nonfatal traumas annually. The Georgia community police department gave away helmets as well as impounding bicycles of those not wearing helmets. A check two years later found that helmet use was at 54 percent. Assume for purposes of this problem the sample size (not given in the article) was 52. Test your hypothesis at the 1% significance level. What is the null hypothesis?

(_) =4

(_) p=.54

(_) p>.25

(o) p=.25
What is the alternative hypothesis?

(_) p<.54

(_) p=.54

(_) p=.25

(_) < 4

(_) p>.54

(_) p<.25

(_) > 4

(o) p>.25
What is the test statistic? [4.83]
What is the p-value? [0]


What probability is the p-value?

(_) The probability the true percentage is 25%.

(_) The probability of seeing a sample percentage of 25% or more if the true percentage is 54%.

(_) The probability the true percentage is 54%.

(_) The probability the sample percentage is 54%.

(_) The probability the true percentage is not 25%.

(o) The probability of seeing a sample percentage of 54% or more if the true percentage is 25%.

Should you reject the null or not?

(_) Do not reject the null

(o) Reject the null

What conclusion can you make?

(_) There is not evidence that helmet use is greater than 25%.

(o) There is evidence that helmet use is greater than 25%.

(_) There is evidence that helmet use is 54%

What is a Type I error for this problem?

(o) Conclude the program is effective when it is not.

(_) Conclude the program is not effective when it is.

What is a Type II error for this problem?

(_) Conclude the program is effective when it is not.

(o) Conclude the program is not effective when it is.

What is the probability of a Type I error?

(_) 0%

(_) 99%

(o) 1%

(_) Need more information to compute it.

What is the probability of a Type II error?

(_) 99%

(_) 0%

(o) Need more information to compute it.

(_) 1%
 

Assume that it is known that 20% of children who sleep with the lights off later develop myopia (near-sightedness). Some studies have suggested that children who sleep with the lights on as infants have a higher rate of myopia. An Ohio State study ( Sleeping With the Lights On , AP, 5/31/00) found the percentage of children who slept in a fully lit room and later became nearsighted was "essentially the same" at 22 percent. Assume for purposes of this problem the sample size (not given in the article) was 269 . Test your hypothesis at the 10% significance level. Does your conclusion agree with theirs?

What is the null hypothesis?

(_) p<.22

(_) p>.20

(_) p>.22

(_) p=.22

(_) p<.20

(o) p=.20

What is the alternative hypothesis?

(_) p>.22

(_) p=.20

(o) p>.20

(_) p<.20

(_) p.20

(_) p=.22

(_) p<.22

What is the test statistic? [0.82]
What is the p-value? [0.206]


What probability is the p-value>

(_) The probability the true percentage is 22%.

(o) The probability of seeing a sample percentage of 22% or more if the true percentage is 20%.

(_) The probability of seeing a sample percentage of 20% or more if the true percentage is 22%.

(_) The probability the sample percentage is 22%.

(_) The probability the true percentage is not 20%.

(_) The probability the true percentage is 20%.

Should you reject the null or not?

(o) Do not reject the null

(_) Reject the null

What conclusion can you make?

(_) There is evidence that children who sleep with a light on have a higher rate of myopia..

(o) There is not evidence that children who sleep with a light on have a higher rate of myopia..

What is a Type I error for this problem?

(_) Conclude that sleeping with a night light on does not causes myopia when it does.

(o) Conclude that sleeping with a night light on causes myopia when it doesn't.

What is a Type II error for this problem?

(_) Conclude that sleeping with a night light on causes myopia when it doesn't

(o) Conclude that sleeping with a night light on does not causes myopia when it does.

What is the probability of a Type I error?

(o) 10%

(_) Need more information to compute it.

(_) 90%

(_) 22%

(_) 20%

What is the probability of a Type II error?

(_) 90%

(o) Need more information to compute it.

(_) 20%

(_) 22%

(_) 10%
 

After a new method of processing wafers was introduced into a fabrication process, 200 wafers were tested, and 16 showed some type of defect. In the past, the fabrication process produced wafers with 10% defectives. The issue is whether the new process has improved the quality of the wafers. Test your hypothesis at the 5% significance level.

What is the null hypothesis?

(_) p .10

(o) p=.10

(_) 16

(_) = 16

What is the alternative hypothesis?

(o) p<.10

(_) p=.10

(_) 16

(_) > 16

(_) < 16

(_) p>.10

(_) p .10

What is the test statistic? [-0.943]
What is the p-value? [0.173]


What probability is the p-value?

(_) The probability the sample percentage is 8%.

(_) The probability of seeing a sample percentage of 10% or more if the true percentage is 8%.

(_) The probability the true percentage is 8%.

(_) The probability the true percentage is not 10%.

(o) The probability of seeing a sample percentage of 8% or less if the true percentage is 10%.

(_) The probability the true percentage is 10%.

Should you reject the null or not?

(_) Reject the null

(o) Do not reject the null

What conclusion can you make?

(_) There is evidence that the quality has improved.

(o) There is not evidence that quality has improved..

What is a Type I error for this problem?

(o) Conclude the new method improved the quality when it did not.

(_) Conclude the new method did not improve the quality when it did.

What is a Type II error for this problem?

(_) Conclude the new method improved the quality when it did not.

(o) Conclude the new method did not improve the quality when it did

What is the probability of a Type I error?

(_) 95%

(_) 10%

(o) 5%

(_) Need more information to compute it.

What is the probability of a Type II error?

(o) Need more information to compute it.

(_) 5%

(_) 95%

(_) 10%
 

The article Body-Piercing Nightmares (Robin Eisner , abcnews.com, 9/27/2000) reports that in a survey of the medical literature, a researcher found an overall 22 percent infection rate for body piercings. Suppose you want to test if the infection rate in Maine is any different than reported in the national study, so you collect a random sample of 50 body-piercings. In your sample you find that 12 of these piercings became infected. Test your hypothesis at the 5% significance level.

What is the null hypothesis?

(_) p<.22

(_) p>.22

(_) p .22

(o) p=.22

(_) 12

(_) > 12

(_) < 12

What is the alternative hypothesis?

(_) p > .22

(o) p .22

(_) = 12

(_) 12

(_) p>.22

(_) > 12

(_) p=.22

(_) < 12

What is the test statistic? [0.34]
What is the p-value? [0.733]


What probability is the p-value?

(o) The probability of seeing a sample percentage of 24% or more if the true percentage is 22%.

(_) The probability the true percentage is 22%.

(_) The probability the true percentage is not 22%.

(_) The probability the sample percentage is 24%.

(_) The probability the true percentage is 24%.

(_) The probability of seeing a sample percentage of 22% or more if the true percentage is 24%.

Should you reject the null or not?

(_) Reject the null

(o) Do not reject the null

What conclusion can you make?

(_) There is evidence that rate of infection is different in Maine.

(o) There is not evidence that the rate of infection is different in Maine.

What is a Type I error for this problem?

(_) Conclude the rate of infection is not different, when it is.

(o) Conclude the rate of infection is different, when it is not.

What is a Type II error for this problem?

(o) Conclude the rate of infection is not different, when it is.

(_) Conclude the rate of infection is different, when it is not.

What is the probability of a Type I error?

(_) Need more information to compute it.

(_) 10%

(o) 5%

(_) 95%

What is the probability of a Type II error?

(o) Need more information to compute it.

(_) 5%

(_) 10%

(_) 95%
 

a. The new idea, a change in the population is stated in which hypothesis?

(o) Alternative

(_) Null

b. If the p-value is less than 0.01, then there is statistical significance at the 0.05 level.

(o) True

(_) False

c. To calculate the p-value one of the things you must know is if the test is one-sided to the right, one-sided to the left, or two-sided.

(o) True

(_) False

d. The p-value can be determined without observing the data.

(_) True

(o) False
e. If the p-value is less than 0.10, then there is statistical significance at the 0.05 level.

(_) True

(_) False

(o) Maybe yes, Maybe not
 

a. Hypotheses are statements about ____________.

(o) Population parameters

(_) Sample statistics

b. When performing the calculations for a hypothesis test, we start off assuming the ______________ hypothesis is true.

(o) Null

(_) Alternative

c. The level of significance is the probabiltiy of

(o) Rejecting the null hypothesis when is true.

(_) Not rejecting the null hypothesis when it is true.

(_) Rejecting the null hpyothesis when it is false.

(_) Not rejecting the null hypothesis when it is false.

d. What is the p-value?

(_) The probability that you should reject the null hypothesis.

(_) The probability that the alternative hypothesis is true.

(_) The probability that the null hypothesis is true.

(o) The probability of seeing the sample data or more extreme if the null hpyothesis is true.

e. Type I error equals

(_) 1 - the p-value.

(_) 1 - Type I error.

(o) The level of significance.

(_) 1 - the level of significance.

(_) The p-value.

(_) Depends on a specific alternative.

f. Type II error equals

(_) 1 - Type I error.

(_) 1 - the p-value.

(_) The level of significance.

(o) Depends on a specific alternative.

(_) The p-value.

(_) 1 - the level of significance.

g. Increasing Type I error

(o) Decreases Type II error.

(_) Increases Type II error.

h. Increasing the sample size

(_) Decreases Type I error.

(_) Decreases both Type I and Type II error.

(o) Decreases Type II error.