Biostatistics in Healthcare
1.The EPA claims that fluoride in children’s drinking water should be at a mean level of less than 1.2 ppm, or parts per million, to reduce the number of dental cavities. Identify the Type I error. (Points : 1)
Fail to support the claim σ < 1.2 when σ < 1.2 is true.
Support the claim μ < 1.2 when μ = 1.2 is true.
Support the claim σ < 1.2 when σ = 1.2 is true.
Fail to support the claim μ < 1.2 when μ < 1.2 is true.
- 2. Biologists are investigating if their efforts to prevent erosion on the bank of a stream have been statistically significant. For this stream, a narrow channel width is a good indicator that erosion is not occurring. Test the claim that the mean width of ten locations within the stream is greater than 3.7 meters. Assume that a simple random sample has been taken, the population standard deviation is not known, and the population is normally distributed. Use the following sample data:
3.3 3.3 3.5 4.9 3.5 4.1 4.1 5 7.3 6.2
What is the P-value associated with your test statistic? Report your answer with three decimals, e.g., .987 . (Points : 1)
3.Ophthalmologists studying the treatment of using an infrared laser procedure in ten patients with vision loss caused by dry age-related macular degeneration (AMD) found the following data on visual acuity (VA) before and after the procedure. Assume a .05 significance level to test the claim that there is a difference between the number of VA lines that can be read by individuals before and after the procedure. Also, assume the data consist of matched pairs, the samples are simple random samples, and the pairs of values are from a population having a distribution that is approximately normal.
| Individual | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| VA Lines Read Before | 3 | 4 | 2 | 4 | 5 | 3 | 4 | 5 | 3 | 3 |
| Laser Procedure | ||||||||||
| VA Lines Read After | 4 | 4 | 5 | 5 | 6 | 3 | 7 | 6 | 3 | 5 |
| Laser Procedure | ||||||||||
Construct a 95% confidence interval estimate of the mean difference between the before and after number of visual acuity lines read. Give your answer with two decimals, e.g., (12.34,56.78) (Points : 1)
4.The paired data consist of the cost of regionally advertising (in thousands of dollars) a certain pharmaceutical drug and the number of new prescriptions written (in thousands).
| Cost | 9 | 2 | 3 | 4 | 2 | 5 | 9 | 10 |
| Number | 85 | 52 | 55 | 68 | 67 | 86 | 83 | 73 |
Find the value of the linear correlation coefficient r . Give your answer to three decimals, e.g., .987 . (Points : 1)
- Use a .05 significance level and the observed frequencies of 144 drownings at the beaches of a randomly selected coastal state to test the claim that the number of drownings for each month is equally likely.
| Jan | Feb | Mar | Apr | May | June | July | Aug | Sept | Oct | Nov | Dec |
| 1 | 3 | 2 | 7 | 14 | 20 | 37 | 33 | 16 | 6 | 2 | 3 |
Do you reject the null hypothesis, at the .05 significance level? Enter Y for yes (reject), N for no (fail to reject). (Points : 1)
- Using a .01 significance level, test the claim that the proportions of fear/do not fear responses are the same for male and female dental patients.
Gender
| Male | Female | |
| Fear Dentistry | 48 | 70 |
| Do Not Fear Dentistry | 21 | 32 |
Do you reject the null hypothesis, at the .01 significance level? Enter Y for yes (reject), N for no (fail to reject). (Points : 1)
- The table represents results from an experiment with patients afflicted in both eyes with glaucoma. Each patient was treated in one eye with laser surgery and in the other eye was treated with eye drops. Using a .05 significance level, apply McNemar’s test to test the following claim: The proportion of patients with no improvement on the laser treated eye and an improvement on the drops treated eye is the same as the proportion of patients with an improvement on the laser treated eye and no improvement on the drops treated eye.
| Eye Drop Treatment |
| Improvement | No Improvement | ||
| Laser Surgery | Improvement | 15 | 10 |
| Treatment | No Improvement | 50 | 25 |
Determine the value of the χ2 test statistic. Give your answer to two decimals, e.g., 12.34 . (Points : 1)
- For a study on Type 1 diabetes, medical graduate students subdivided the United States into four study regions (Northeast, Southeast, Southwest, and Northwest). The students randomly selected seven patients per region and recorded the number of times during a randomly selected month that each patient used insulin shots to regulate blood sugar levels. Use One-Way ANOVA at a .05 significance level to test the claim that the means from the different regions are not the same.
Mean number of times patients used insulin shots to regulate blood sugar levels
| Northeast | Southeast | Southwest | Northwest |
| 4 | 6 | 4 | 4 |
| 3 | 5 | 5 | 4 |
| 3 | 6 | 6 | 5 |
| 4 | 8 | 6 | 6 |
| 3 | 6 | 7 | 3 |
| 2 | 6 | 5 | 5 |
| 5 | 8 | 4 | 3 |
Do you reject the null hypothesis, at the .05 significance level? Enter Y for yes (reject), N for no (fail to reject). (Points : 1)
- 9. One method to reduce the effect of extraneous factors is to design the experiment so that it has a convenience sampling design. (Points : 1)
True
False
- Use the following technology display from a Two-Way ANOVA to answer this question. Biologists studying habitat use in Lepidopteran moths measured the number of savannah moths found at three randomly selected prairie sites with two potential habitat interferences (expansion of row crops and grazing). Use a .05 significance level.
| Source | Df | SS | MS | F | P |
| Site | 2 | .1905 | .0952 | .0381 | .9627 |
| Habitat | 1 | 304.0238 | 304.0238 | 121.6095 | .0000 |
| Site*Habitat | 2 | .1905 | .0952 | .0381 | .9627 |
Do you reject the null hypothesis anbout the habitat effect, at the .05 significance level? Enter Y for yes (reject), N for no (fail to reject). (Points : 1)