question archive a) A company produces precision 1-meter (1000 mm) rulers
a) A company produces precision 1-meter (1000 mm) rulers
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a) A company produces precision 1-meter (1000 mm) rulers. The actual distribution of lengths of the rulers produced by this company is normal with mean m and standard deviation 0.02 mm.
Suppose I select a simple random sample of four of the rulers produced by the company and I measure their lengths in millimeters. The results of these four measurements are as follows.
1,000.01 999.98 1,000.00 1,000.01
Estimate the mean length of 1 meter rulers
This is a: Single sample Z-procedure- hypothesis test; single sample Z-procedure- confidence interval; single sample Z- procedure- confidence interval; or single sample t- procedure- hypothesis test.
b) A company produces precision 1-meter (1000 mm) rulers. The actual distribution of lengths of the rulers produced by this company is normally distributed. Suppose I select a simple random sample of four of the rulers produced by the company and I measure their lengths in millimeters. The results of these four measurements are as follows.
1,000.01 999.98 1,000.00 1,000.01
We want to prove that the average length of the rulers is not equal to 1 meter.
This is a: Single sample Z-procedure- hypothesis test; single sample Z-procedure- confidence interval; single sample Z- procedure- confidence interval; or single sample t- procedure- hypothesis test.
3. In a national vocabulary test, it is known that the mean score is 68 and the standard deviation is 13.
A class of 20 students takes the test and has a mean score of 64. Is it true that that the average of this class is significantly lower than the national average?
This is a: Single sample Z-procedure- hypothesis test; single sample Z-procedure- confidence interval; single sample Z- procedure- confidence interval; or single sample t- procedure- hypothesis test.
4. In national vocabulary test, a class of 150 students takes the test and has a mean score of 64 and a standard deviation of 13. What is the average score on this national vocabulary test?
This is a: Single sample Z-procedure- hypothesis test; single sample Z-procedure- confidence interval; single sample Z- procedure- confidence interval; or single sample t- procedure- hypothesis test.
5. In a clinical trial, 25 subjects are given the brand name drug and another group of 20 subjects are given a generic drug. We want to prove that the brand name drug is significantly more effective than the generic drug.
This is a: Matched pair confidence interval; two- sample confidence interval; two- sample hypothesis test; or matched pairs hypothesis test.
6. In a clinical trial, 25 subjects are given the brand name drug for the first two weeks and the generic drug generic drug for the next two weeks. We want to find the mean difference in the time that it takes to clear the symptoms of flu.
This is a: Matched pair confidence interval; two- sample confidence interval; two- sample hypothesis test; or matched pairs hypothesis test.
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(a) Single sample Z-procedure- confidence interval
(b) Single sample t- procedure- hypothesis test.
(3) Single sample Z-procedure- hypothesis test
(4) Single sample t-procedure- confidence interval
(5) two- sample hypothesis test
(6) Matched pair confidence interval
Step-by-step explanation
(a) Population standard deviation is known and we are asked to estimate the mean length of 1 meter rulers. In case of estimation, we always calculate confidence interval.
Here, we will use single sample Z-procedure- confidence interval because ?σ? is known.
(b) Population standard deviation is unknown and we are asked to prove that the average length of the rulers is not equal to 1 meter. In case of prove, we always conduct hypothesis testing.
Here, we will use single sample t- procedure- hypothesis test because ?σ? is unknown and sample size is small.
(3) Population standard deviation is known and we are asked to test if the average of given class is significantly lower than the national average. In case of claim testing, we always conduct hypothesis testing.
Here, we will use single sample z- procedure- hypothesis test because ?σ? is known.
(4) Population standard deviation is unknown and we are asked to estimate the average score on national vocabulary test. In case of estimation, we always calculate confidence interval.
Here, we will use single sample t-procedure- confidence interval because ?σ? is unknown and sample size is large.
(5) It is given that 25 subjects are given the brand name drug and another group of 20 subjects are given a generic drug. So, we have two independent samples and we need to test whether the brand name drug is significantly more effective than the generic drug, i.e. ?μbrand name?−μgeneric drug?>0?
So, it is a case of hypothesis testing and we will conduct two- sample hypothesis test
(6) it is given that 25 subjects are given the brand name drug for the first two weeks and the generic drug generic drug for the next two weeks. So, we have two dependent samples and we need to estimate the mean difference
So, we will use Matched pair confidence interval
