Task 2. A total of 678 women, who got pregnant under planned pregnancies, were asked how many cycles it took them to get pregnant. The women were classified as smokers and nonsmok- ers; it is of interest to compare the association between smoking and probability of pregnancy. The following table (Weinberg and Gladen, 1986, “The Beta-Geometric Distribution Applied to Comparative Fecundability Studies", Biometrics 42(3): 547–560) summarises part of the data (essentially, women who had used the pill as a contraceptive are excluded). Observed cycles to pregnancY Non- Non- Cycle Smokers smokers Cycle Smokers smokers 1 29 198 8 5 9 16 107 9. 1 3 17 55 10 1 4 4 38 11 1 3 18 12 3 6 6. 9. 22 >12 7 12 7 4 7

5.28 Risks and insurance. The idea of insurance is that we all face risks that are unlikely but carry high cost. Think of a fire destroying your home. So we form a group to share the risk: we all pay a small amount, and the insurance policy pays a large amount to those few of us whose homes burn down. An insurance company looks at the records for millions of homeowners and sees that the mean loss from fire in a year is μ = $250 per house and that the standard deviation of the loss is σ = $1000. (The distribution of losses is extremely right-skewed: most people have $0 loss, but a few have large losses.) The company plans to sell fire insurance for $250 plus enough to cover its costs and profit. If the company sells 25,000 policies, what is the approximate probability that the average loss in a year will be greater than $270?

An investigation is performed to evaluate two new experimental treatments for allergies. 18 subjects who suffer from allergies are enrolled in the study and randomly assigned to one of three treatments: Control Group, Experimental Treatment 1, or Experimental Treatment 2. Each subject is instructed to take the assigned treatment, and symptoms of allergies are recorded on a scale of 1 to 20, with higher scores indicating worse symptoms. The data is summarized in the table below: SBP Std. Deviation Group Mean Control Treatment 6. 16.17 2.483 Experimental Treatment 1 6. 11.33 1.966 Experimental Treatment 6. 3.83 1.472 Total 18 10.44 5.554 Use this data to complete an ANOVA table to test for a significant difference in the means of each of the groups. Round all answers to the third decimal point.

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…

Statistical Methods in Atmospheric Science

Does buttered toast fall face down? Data was collected to test this. 40 slices of toast (each with butter on one side) were dropped (from the same height). 24 slices (60%) landed buttered side down. We would like to use the results of this study to determine if there is statistical evidence that toast tends to land buttered side down more than 50% of the time.

A researcher was interested in comparing the resting pulse rate of people who exercise regularly and people who do not exercise regularly. Independent random samples of 16 people aged 30-40 who do not exercise regularly (sample 1) and 12 people aged 30-40 who do exercise regularly (sample 2) were selected and the resting pulse rate of each person was measured. The summary statistics are as follows: Pulse Rate data   Group 1 (no exercise) Group 2 (exercise) average 72.7 69.7 standard deviation 10.9 8.2 sample size 16 12 Test the claim that the mean resting pulse rate of people who do not exercise regularly is greater than the mean resting pulse rate of people who exercise regularly, use 0.01 as the significance level. Round you answer to 3 decimal places. Group of answer choices p-value=0.207, evidence not support claim p-value=0.267, evidence support claim p-value=0.414, evidence not support claim p-value=0.793, evidence not support claim p-value=0.207, evidence…

The article “Well-Fed Crickets Bowl Maidens Over” (Nature Science Update, February 11, 1999) reported that female field crickets are attracted to males with high chirp rates and hypothesized that chirp rate is related to nutritional status. The usual chirp rate for male field crickets was reported to vary around a mean of 60 chirps per second. To investigate whether the chirp rate was related to nutritional status, investigators fed 22 male crickets a high protein diet for 8 days, after which chirp rate was measured. Let:  The parameter μμ be the mean chirp rateof male crickets on a high protein diet for 8 days.    Given: The mean chirp rate for the random sample of crickets on the high protein diet was reported to be 65.32 chirps per second with a standard deviation of 12. Research Question: Is there convincing evidence that the mean chirp rate for crickets on a high protein diet implies an advantage in attracting the ladies? It is known that the researchers did not want to…

As a hospital administrator of a large hospital, you are concerned with the absenteeism among nurses' aides. The issue has been raised by registered nurses, who feel they often have to perform work normally done by their aides. To get the facts, absenteeism data were gathered for the last three weeks, which is considered a representative period for future conditions. After taking random samples of 64 personnel files each day, the following data were produced: Because your assessment of absenteeism is likely to come under careful scrutiny, you would like a type I error of only 1 percent. You want to be sure to identify any instances of unusual absences. If some are present, you will have to explore them on behalf of the registered nurses. a. Design a p-chart. The upper control limit is enter your response here and the lower control limit is enter your response here . (Enter your responses rounded to three decimal places. If your answer for the lower control limit is negative, enter…