Serum estradiol is an important risk factor for breast cancer in postmenopausal women. To better understand the etiology of breast cancer, serum-estradiol samples were collected from 25 premenopausal women (at about the same time period of the menstrual cycle) of whom 10 were Caucasian and 15 were African American. The data are shown in Table 7.3. The distribution of serum estradiol is usually highly skewed (especially for premenopausal women), and we are reluctant to assume normality. Table 7.3 Serum estradiol and ethnicity in 25 premenopausal women, where 0=Caucasian and 1=African-American ID Serum_estradiol Ethic 1 94 0 2 54 1 3 31 0 4 21 1 5 46 1 6 56 0 7 18 1 8 19 1 9 12 1 10 14 0 11 25 0 12 35 1 13 22 1 14 71 0 15 43 1 16 35 1 17 42 1 18 50 1 19 44 1 20 41 0 21 28 0 22 65 0 23 31 0 24 35 1 25 91 1 7.1: What test  can we use (Sign test, or Wilcoxon signed-rank test or Wilcoxon rank-sum test) to compare the distribution of serum estradiol for Caucasian vs. African American women? Implement the test in Problem 7.1, and report a two-tailed p-value based on large sample methods.

5.20 High School and Beyond, Part I:  The National Center of Education Statistics conducted a survey of high school seniors, collecting test data on reading, writing, and several other subjects. Here we examine a simple random sample of 200 students from this survey. Side-by-side box plots of reading and writing scores as well as a histogram of the differences in scores are shown below.   (a) Are the reading and writing scores of each student independent of each other? ( )yes, they are paired since each student has both a reading score and a writing score ( )no, they are paired since each student has both a reading score and a writing score ( ) yes, because reading and writing are two different activities (b) Create hypotheses appropriate for the following research question: is there an evident difference in the average scores of students in the reading and writing exam? ( )Ho: μdiff = 0Ha: μdiff < 0 ( )Ho: μdiff = 0Ha: μdiff > 0 ( )Ho: μdiff = 0Ha: μdiff ≠ 0 (c) The…

A case-control study is conducted to assess the relationship between heavy alcohol use during the first trimester of pregnancy and miscarriage.  Fifty women who suffered miscarriage are enrolled along with 50 who delivered full term.  Each participant’s use of alcohol during pregnancy is ascertained.  Heavy drinking is defined as 4 or more drinks on one occasion.  The data are shown below.     Miscarriage Delivered Full Term Heavy Alcohol Use 14 4 No Heavy Alcohol Use 36 46   Compute the odds of miscarriage among women with heavy alcohol use in pregnancy.

In an investigation of the visual scanning behaviour of deaf children, measurements of eye movement rates were taken on nine deaf and nine normal children as shown in the table below Deaf Children Normal Children 1.81 0.95 2.2 1.49 3.29 1.12 2.13 1.07 2.55 1 2.24 1.85 2.22 1.18 2.89 2.07 2.26 1.18 a. If the two samples are drawn from normal populations, test the hypothesis that on average eye movement rate for normal children is less than deaf children in the population at a 10% level of significance. b. What does the 10% level of significance mean? Does it appear that the distributions of eye-movement rates for deaf children and normal children differ at 5% level of significance (assuming samples are not drawn from normal population)? с.

Water availability is of prime importance in the life cycle of most reptiles. To determine the rate of evaporative water loss of a certain species of lizard at a particular desert site, 34 such lizards were randomly collected, weighed and placed under the appropriate experimental conditions. After 24 hours, each lizard was removed, weighed, and its total water loss was calculated by subtracting its body weight after treatment from its initial body weight. Previous studies have shown that the relative frequency distribution of water loss for this species of lizard has a mean of 3.1 grams and a s.d. of 0.8 gram. a) What is the approximate sampling distribution of x , the mean water loss of the 34 lizards

Suppose a neighborhood has few very expensive homes and many low value homes. Which measure of central tendency a. would give the highest "average"? Why? b. would give the lowest "average"? Why? c. would be the most representative "average"? Why?

Serum estradiol is an important risk factor for breast cancer in postmenopausal women. To better understand the etiology of breast cancer, serum-estradiol samples were collected from 25 premenopausal women (at about the same time period of the menstrual cycle) of whom 10 were Caucasian and 15 were African American. The data are shown in Table 7.3. The distribution of serum estradiol is usually highly skewed (especially for premenopausal women), and we are reluctant to assume normality. Table 7.3 Serum estradiol and ethnicity in 25 premenopausal women, where 0=Caucasian and 1=African-American. ID Serum_estradiol Ethic 1 94 0 2 54 1 3 31 0 4 21 1 5 46 1 6 56 0 7 18 1 8 19 1 9 12 1 10 14 0 11 25 0 12 35 1 13 22 1 14 71 0 15 43 1 16 35 1 17 42 1 18 50 1 19 44 1 20 41 0 21 28 0 22 65 0 23 31 0 24…

A study is performed to assess the prevalence of use of anti-hypertensive medication (MEDS) in the non-institutionalized U.S. population. The following data are reported for MEDS status of the U.S. population by age-sex group:   Table 1   Estimated MEDS Status of the U.S. Population by age and sex group, NHANES study 1999-2018     Males       Females   Age Group MEDS = yes Na   Age Group MEDS = yes Na 18-29 160,617 23,069,867   18-29 168,940 22,132,949 30-39 899,152 18,690,754   30-39 759,532 18,937,878 40-49 2,264,304 18,316,125   40-49 2,257,203 18,816,304 50-59 3,215,688 15,022,905   50-59 4,059,363 15,997,653 60-69 2,936,183 8,400,156   60-69 4,260,975 10,993,805 70-79 1,677,664 4,012,930   70-79 2,953,646 6,012,728   aN = total sample size in specific age-sex groups.   a. What is the prevalence of use of MEDS in 40-49 year-old females? b. Suppose a married couple consists…

The following is data about the hemoglobin concentrations of volunteers collected at sea level and at an altitude of 11000 feet. sea level concentrations = [14.70 , 15.22, 15.28, 16.58, 15.10 , 15.66, 15.91, 14.41, 14.73, 15.09, 15.62, 14.92]11000 feet concentrations = [14.81, 15.68, 15.57, 16.59, 15.21, 15.69, 16.16, 14.68, 15.09, 15.30 , 16.15, 14.76] There are two alternative scenarios about the way the data were obtained. In scenario 1, there are 12 volunteers who lived for a month at sea level, at which time blood was drawn and the data in "sea level concentrations" dataset were obtained.  Subsequently, all 12 volunteers were moved to 11000 ft and after a month the data in the "11000 feet concentrations" dataset obtained.  There is a one to one correspondence between the numbers in the two datasets, that is the first numbers correspond to volunteer1, the second numbers to volunteer2 etc. In scenario 2, the "sea level concentrations" dataset  is a random sample obtained from 12…

Child Health and Development Studies (CHDS) has been collecting data about expectant mothers in Oakland, CA since 1959. One of the measurements taken by CHDS is the weight increase (in pounds) for expectant mothers in the second trimester. In a fictitious study, suppose that CHDS finds the average weight increase in the second trimester is 14 pounds. Suppose also that, in 2015, a random sample of 40 expectant mothers have mean weight increase of 15.8 pounds in the second trimester, with a standard deviation of 6.2 pounds. A hypothesis test is done to see if there is evidence that weight increase in the second trimester is greater than 14 pounds. Find the p-value for the hypothesis test.  The p-value should be rounded to 4 decimal places.