Math 221
Week 6 Lab
Submitted by: Merima Ceric
Part 1. Normal Distributions and Birth Weights in America
1) What percent of the babies born with each gestation period have a low birth weight (under 5.5 pounds)? a) Under 28 = 99.88% The NORMDIST formula was used to calculate: =NORMDIST(5.5,1.88,1.99,True) X= 5.5 Mean= 1.88 Standard Deviation=1.19
b) 32 to 35 weeks = 43.83% The NORMDIST formula was used to calculate: =NORMDIST (5.5,5.73,1.48,True) X= 5.5 Mean= 5.73 Standard Deviation=1.48
c) 37 to 39 weeks = 4.66% The NORMDIST formula was used to calculate: =NORMDIST(5.5,7.33,1.09, True) X= 5.5 Mean= 7.33
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3) No, the ages are not normally distributed because with the view of the histogram, it is not bell shaped.
4)
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Histogram is approximately bell shaped and symmetric and agrees with the results predicted by the Central Limit Theorem which says that whatever the population shape, the sampling distribution is approximately normal
5) Standard deviation = 3.5518 ( = STDEV formula was used) Standard deviation of population = 22.57 Standard deviation of sample mean=Standard deviation / sqauare root of sample size = 40 Therefore Standard deviation of sample mean= 3.567841 These two values are close; thus the result predicted by central limit theorem is true.
Part 3. Finding z- and t-scores for Confidence Intervals
1. Using Excel, find the z-score that corresponds to the following Confidence Levels:
a. 80%
Confidence level = 80% or Significance
The histogram has one spike that shows that high concentration of data values is below this point. This histogram might be representing a seasonal product, which customers are ordering high volume of product until they run out and order one more time. Also it might be showing the histogram of a car brand were less expensive cars are sold frequently, but in average the middle range cars are bringing to the company more capital and high luxury cars are sold more expensive and less frequently.
5. In HANESS, the men age 18 and over had an average height of 69 inches and an SD of 3 inches. The histograms is show below, with a normal curve. The percentage of men with heights between 66 inches and 72 inches is exactly equal to the area between (a) and (b) under (c). This percentage is approximately equal to the area between (d) and (e) under the (f). Fill in the blanks.
Since in a normal distribution, the curve is symmetrical, skewness can affect the accuracy to which normal distribution can be applied to a data set. To determine how close the distribution of the weight of the AFL population is to being normal, the degree of skewness was found as a large degree of skewness would reduce the practicality of applying normal distribution to the data set.
10. Identify whether these distributions are negatively skewed, positively skewed, or not skewed at all, and why.
7. Question : In a frequency distribution such as a bell-shaped curve, what does the vertical height of the curve indicate?
Please check your numbers again, some of them seem incorrect. For example, how is that possible the subset has a more extended age range than the total sample?
The amount of time it takes to recover physiologically from a certain kind of sudden noise is found to be normally distributed with a mean of 80 seconds and a standard deviation of 10 seconds. Using the 50%–34%–14% figures, approximately what percentage of scores (on time to recover) will be:
Explain. I don’t think that mine has normal distribution. Mine has a wide range of numbers, but I don’t think that it is distributed like a normal graph should be distributed
Discuss disparities related to ethnic and cultural groups relative to low birth weight infants and preterm births.
i) How does the shape of the distribution impact what you conclude? The shape distribution is out of range.
-The shape of both data sets fall within the rule of thumb estimate and that actual standard deviation. There is a much high range for both and that is because there are several data samples that fall outside of the standard deviation.
The standard Deviation comparing both sets of data only shows a slight difference on the numbers (a difference of only 1.38187054), but in the histograms both show a huge difference on the frequencies of each data set, but shows a similarity on the cumulative percentage. Data set #2 seem to be more stable even though the grades of the student were lower than data set #1. Data set#2 shows a relative stability in regards the frequency on the histograms, when comparing the frequency histograms data set #2 has more frequency on number two’s than data set #1 on frequency on the number three’s. In this case Data set #2 shows a normal distribution behavior.
COMMENTS argument is that because the average effect size for published research was equivalent to that of a medium effect, the reviewer 's decision to reject the bogus manuscript under the nonsignificant condition was "reasonable." Further examination of the Haase et al. (1982) article and our own analysis of published research, however, demonstrates that the power of the bogus study was great enough to detect effect sizes that are typical of research published in JCP, which was our intention when we designed the bogus study. First, although the median effect size (if) for all univariate statistical tests, significant and nonsignificant, reported by Haase et al. (1982) was .083, this index was steadily increasing at a rate of approximately .5% per year, so that the projected median if- in 1981 (the year our study was completed) would be .13. Importantly, an r)2 of .13 corresponds to an effect size (/) of .39, which Cohen (1977) designates as a large effect. A further examination of the Haase et al. (1982) data also lends support to our argument. Their analysis examined the strength of association for 11,044 univariate statistical tests derived from only 701 manuscripts; thus, each manuscript reported an average of more than 15 statistical tests. Since statistically significant and
Based on the above, it appears that the assumptions have been met. Assumption 1, that the outcome variable will be normally distributed, is supported by visual interpretation of the histogram and the skewness and kurtosis calculations. The Shapiro-Wilk test, on the other hand, did not support the assumption. However, this could be due to sample size; the bigger the sample, the more accurate the results. This could shed some doubt on the research; to completely meet the assumption, a larger
While some women who received no prenatal care had normal, uncomplicated births, others did not. Most of the women who did not receive adequate prenatal care gave birth to an underweight and underdeveloped infant. Among the benefits of early, comprehensive prenatal care are decreased risk of preterm deliveries and low birth weight (LBW)-both major predictors of infant morbidity and mortality. (Dixon, Cobb, Clarke, 2000). Preterm deliveries, deliveries prior to 37 weeks of gestation, have risen. Since the studies in 1987, which showed the rate of preterm deliveries as 6.9% of births, the 1997 rate shows an increase to 7.5%. Low birth weight, defined as an infant weighing less than 2500 grams (5lbs. 5oz) is often preceded by preterm delivery. Low