Question

A group of veterinary researchers plan a study to estimate the average number of enteroliths in horses suffering from them. Previously research has shown the variability in the number to be σ = 2. The researchers wish the margin of error to be no larger than 0.5 for a 99% confidence interval. To obtain such a margin of error the researchers need at least:

A. 53 observations.
B. 107 observations.
C. 106 observations.
D. 54 observations.
2.

A group of veterinary researchers plan a study to estimate the average number of enteroliths in horses suffering from them. The number of enteroliths is determined by surgery or ultrasound. This requires the participation of a radiologist and a surgeon in the study. The researchers decide that they should only enroll horses seen at the best veterinary hospital in the country to ensure correct counts. Such a hospital will typically see the most severe cases. The researchers will enroll the first 100 horses seen beginning on the day the study is funded. The resulting interval is likely biased because:
A. the first 100 horses seen is not an SRS of all horses with enteroliths and therefore never representative.
B. a sample of 100 horses is too small to obtain an unbiased estimate.
C. the best veterinary hospital is likely to see the most severe cases with larger number of enteroliths.
D. All of the above

3.

A group of veterinary researchers plan a study to estimate the average number of enteroliths in horses suffering from them. The number of enteroliths is determined by surgery or ultrasound. This requires the participation of a radiologist and a surgeon in the study. The researchers decide that they should only enroll horses seen at the best veterinary hospital in the country to ensure correct counts. Such a hospital will typically see the most severe cases. The researchers will enroll the first 20 horses seen beginning on the day the study is funded. The researchers will calculate a 95% confidence interval. The procedure is not valid because the:
A. sample size is too small for the central limit theorem to apply.
B. average number is not an integer and does not reflect any actual observation.
C. None of the above. The procedure is valid.
D. data are counts and, therefore, not Normally distributed.

4.

In a test of hypothesis for a mean, which statement is CORRECT?
A. The test requires that the sample mean is normally distributed; this requires that either the population distribution is Normal or the sample size exceeds 30.
B. As long as the population distribution consists only of positive values, sample size does not matter.
C. The population distribution can be any distribution because the sample mean is always Normally distributed.
D. The population must be normal because that is the only case when the sample mean is Normally distributed.

5.

A "false negative," in which no effect is detected when in reality one exists, is an example of:
A. a Type I error.
B. the power of the test.
C. a Type II error.
D. None of the above

Answer 1

1.) 107 observations

2.) the best veterinary hospital is likely to see the most severe cases with larger number of enteroliths

3.) A. sample size is too small for the central limit theorem to apply.

4.) The test requires that the sample mean is normally distributed; this requires that either the population distribution is Normal or the sample size exceeds 30.

5.) a Type I error

Explanation:

n = [(Zcritical * σ) ÷ E]²

n = sample size

Zcritical at 99% = 2.58

E = error margin = 0.5

Standard deviation, σ = 2

n = [(2.58 * 2) ÷ 0.5]²

n = [5.16 ÷ 0.5]²

n = (10.32)²

n = 106.5024

n = 107 observations

B.) The thought or decision that the best veterinary hospital is likely to see the most severe cases with larger number of enteroliths will introduce a bias in the study.

C.) For central limit theorem ; sample size must be considerably large ; at least sample size, n ≥ 30

D.) Distribution must be normal it approximately normal, obeying the central limit theorem ; sample size must be considerably large ; at least sample size, n ≥ 30