STAT 601 – Assignment #7 (Due Wednesday, Oct



STAT 601 – Assignment #6 (Due Friday Oct. 19th – Monday Oct. 22nd )

1 – Serum IgG for Patients with Linear Schleroderma

In a study of linear scleroderma, serum IgG levels were reported for nine patients with inactive disease and 30 patients with active disease. The resulting data are presented below:

Patients with

inactive disease: 680 980 1025 950 840 1250 950 1250 930

Patients with

active disease: 1220 1150 1300 1430 1300 1475 740 1250 1070

800 880 1400 1100 1000 1100 1550 660 820

1250 1400 1950 1200 1850 930 1700 1250 1150

1140 2900 1600

Research Question: Is there evidence to suggest that patients with active linear scleroderma have a higher mean serum IgG level than patients with inactive? 

Use JMP to analyze these data.  You can enter the data in JMP yourself.  You will need two columns, one to denote the disease status and the other to contain the response, in this case serum IgG level.  Be sure to check assumptions and perform your analysis accordingly. 

a) Perform a hypothesis test answer the question of interest and summarize your findings.

(4 pts.)

b) Find and report the 95% CI for the difference in the population means from the JMP output.  Discuss this interval in practical terms. (2 pts.)

2 – Power and Sample Size for Two Sample t-Tests

In order to conduct a larger scale study of blood pressure and oral contraceptive (OC) use

a smaller scale pilot study is conducted in order to help determine needed sample sizes. The researchers would like to have a power of .90 or 90% in detecting a difference of

|μOC – μNon-OC| = 5 mmHg using a test conducted at the α = .05 level. The results from a small pilot study in terms of sample standard deviations are as follows [pic] where sample sizes of n = 10 were used in sampling each population of women. What sample sizes should they use in conducting the larger scale study?

a) First calculate the pooled estimate of the standard deviation (sp) and use this as the Error Std Dev in the Sample Size and Power calculator in JMP. (3 pts.)

b) Now determine what sample size should be used from each population in conducting the larger scale study so that the desired power-related outcomes above are met. (3 pts.)

c) Answer the following True and False questions (1 pt. each)

I. If we use larger sample sizes from each population than the one you found in part

(b) the power would increase.

II. If we decrease α the power will increase.

III. If in reality the population standard deviation common to both populations was

larger than your answer from part (a) then the power would be larger also.

IV. If decided we wanted to detect a difference of 10 mmHg instead of 5 mmHg with

a power of .90 would the sample size needed would be smaller than that found in

part(b).

3 – Comparisons of the Mean Infant Birth Weight for Different Populations of Mothers Data File:  NCBirth.JMP

In this problem you will use comparative methods to compare the actual mean birth weights of different populations of mothers. The results of your comparisons will be contained in the table below. For each situation be sure to check assumptions and briefly summarize your findings in that regard.

[pic]

Use appropriate statistical methods to make comparisons of mean birth weight across the two populations defined by the variables below:

• Sex of child (1 = male, 2 = female)

• Marital status (1 = married, 2 = not married)

• White? (Non-white vs. White)

• Hispanic? (Hisp vs. non-Hisp)

• Smokers vs. non-smokers

a) Use both hypothesis tests and confidence intervals to compare the mean birth weights of the infants born to the two populations defined by the factors above. To organize your results enter them into the table below. For the p-value and CI columns you will need to enter the p-value from the appropriate test for comparing the two population means for each factor and the confidence interval for the difference in those population means, thus for each factor you will only have one p-value and confidence interval. Report the sample size, sample mean, and sample standard deviation (SD) for each level of the factor. (20 pts.)

| | | | | | |

|Factor |Sample |Sample Mean |SD |p-value |CI for Difference in |

| |Size (n) | | | |Population Means |

|Sex of Child | | | | | |

|Male | | | | | |

|Female | | | | | |

|Marital Status | | | | | |

|Married | | | | | |

|Not Married | | | | | |

|White? | | | | | |

|Non-white | | | | | |

|White | | | | | |

|Hispanic? | | | | | |

|Hispanic | | | | | |

|Non-Hispanic | | | | | |

|Smoking Status | | | | | |

|Smoker | | | | | |

|Non-smoker | | | | | |

b) Briefly comment on the assumptions required for the analyses you conducted in completing the table. Are the assumptions satisfied for each factor? (5 pts.)

c) Summarize your findings from part (a) in a clearly written paragraph, citing p-values and confidence intervals as needed. (10 pts.)

4 - Middle Ear Effusion in Breast-Fed and Bottle-Fed Infants

A common symptom of otitus media in young children in the prolonged presence of fluid in the middle ear, known a middle-ear effusion. The presence of fluid may result in termporary hearing loss and interfere with normal learning skills in the first two years of life. One hypothesis is that babies who are breast-fed for at least 1 month build up some immunity against the effects of the disease and have less prolonged effusion than do bottle-fed babies. A small study of 24 pairs of babies is set up, where the babies are matched on a one-to-one basis according to age, sex, socioeconomic status, and type of medications taken. One member of the matched pair is a breast-fed baby, and other member is a bottle fed baby. The outcome variable is the duration of middle-ear effusion after the first episode of otitus media. The results are shown below.

|Pair Number |Duration of effusion in breast-fed baby |Duration of effusion in bottle-fed baby | |

| | | |Difference |

|1 |20 |18 | |

|2 |11 |35 | |

|3 |3 |7 | |

|4 |24 |182 | |

|5 |7 |6 | |

|6 |28 |33 | |

|7 |58 |223 | |

|8 |39 |57 | |

|9 |17 |76 | |

|10 |17 |186 | |

|11 |12 |29 | |

|12 |52 |39 | |

|13 |14 |15 | |

|14 |12 |21 | |

|15 |30 |28 | |

|16 |7 |8 | |

|17 |15 |27 | |

|18 |65 |77 | |

|19 |10 |12 | |

|20 |7 |8 | |

|21 |19 |16 | |

|22 |34 |28 | |

|23 |25 |20 | |

Do these data provide evidence that breast-fed babies have shorter durations of effusion when compared to bottle-fed babies that are the same age, sex, socioeconomic status, and on the same medications? Enter these data into JMP and conduct the appropriate analysis. (6 pts.)

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