04 Jun Question 1. Ginger root is used by many as a dietary supple
Question
1. Ginger root is used by many as a dietary supplement. A manufacturer of
supplements produces capsules that are advertised to contain at least 500 mg.
of ground ginger root. A consumer advocacy group doubts this claim and tests
the hypotheses
H0: ? = 500 Ha: ? < 500 based on measuring the amount of ginger root in a SRS of 100 capsules. Suppose the results of the test fail to reject H0 when, in fact, the alternative hypothesis is true. In this case the consumer advocacy group will have a. committed a Type I error. b. committed a Type II error. c. no power to detect a mean of 500. 2. A researcher reports that a test is "significant at 5%." This test will be a. Significant at 1%. b. Not significant at 1%. c. Significant at 10%. 3. Suppose the average Math SAT score for all students taking the exam this year is 480 with standard deviation 100. Assume the distribution of scores is normal. The senator of a particular state notices that the mean score for students in his state who took the Math SAT is 500. His state recently adopted a new mathematics curriculum and he wonders if the improved scores are evidence that the new curriculum has been successful. Since over 10,000 students in his state took the Math SAT, he can show that the P-value for testing whether the mean score in his state is more than the national average of 480 is less than 0.0001. We may correctly conclude that a. there is strong statistical evidence that the new curriculum has improved Math SAT scores in his state. b. although the results are statistically significant, they are not practically significant, since an increase of 20 points is fairly small. c. these results are not good evidence that the new curriculum has improved Math SAT scores. 4. I want to construct a 92% confidence interval. The correct z* to use is a. 1.75 b. 1.41 c. 1.645 5. The teacher of a class of 40 high school seniors is curious whether the mean Math SAT score ? for the population of all 40 students in his class is greater than 500 or not. To investigate this, he decides to test the hypotheses H0: ? = 500 Ha: ? > 500
at level ? = 0.05. To do so, he computes that average Math SAT score of all the
students in his class and constructs a 95% confidence interval for the population
mean. The mean Math SAT score of all the students was 502 and, assuming the
standard deviation of the scores is ? = 100, he finds the 95% confidence interval is
502 ? 31. He may conclude
a. H0 cannot be rejected at level ? = 0.05 because 500 is within confidence
interval.
b. H0 cannot be rejected at level ? = 0.05, but this must be determined by
carrying out the hypothesis test rather than using the confidence interval.
c. We can be certain that H0 is not true.
6. I wish to find a 95% confidence interval for the mean number of times men
change channels with a remote control during a commercial. Based on a
preliminary study, I estimate ? = 15. How many commercials’ worth of data do
I need to have a margin of error no more than 3?
a. 10
b. 97
c. 96
7. Experiments on learning in animals sometimes measure how long a laboratory
rat takes to find its way through a maze. Suppose for one particular maze, the
mean time is known to be 20 seconds with a standard deviation of = 2
seconds. Suppose also that times for laboratory rats are normally distributed. A
researcher decides to test whether rats exposed to cigarette smoke take longer
on average to complete the maze. She exposes 25 rats to cigarette smoke for 15
minutes and then records how long each takes to complete the maze. The mean
time for these rats is 20.6 seconds. Are these results significant at the =
0.05 level? Assume the researcher’s rats can be considered a SRS from the
population of all laboratory rats.
a. Yes.
b. No.
c. The question cannot be answered since the results are not practically
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