• Two-sample Non-parametric Test
Now, we examine the relationship between cry time and group among infants at Northbay.
1. Suppose we wish to perform a two-sample test, but we do not want to make any normality (or other strong parametric) assumptions. Conduct an appropriate non-parametric test to test whether the distribution of cry time is the same in both groups at the 0.05 level of significance.
What is your p-value?
unanswered
Your conclusion from the test?
there is evidence that the *means* of the two groups are different (specifically, there is evidence that the mean is higher in the control group) there is not evidence that the *means* of the two groups are different none of the above
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• 2. Assuming randomization was successful and all participants complied with their assigned exposure, which of the following should we be concerned about:
Confounding by sex of the infant Confounding by the amount of pain experienced by the infant Effect modification by sex of the infant Misclassification of the exposure status of the infant
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• Exploratory Analysis
Before jumping into analyzing the babies.dta dataset, first explore the dataset using summary statistics and graphical analyses.
1. Make a boxplot of cry time by group. According to the boxplot, which group has more variability in cry time?
control intervention
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• 2. Using the central limit theorem, construct a 95% confidence interval for the average total cry time for infants in the control group and infants in the intervention group. For this question only, assume that the standard deviation of cry time within each group is known and is equal to 22 seconds.
Control
Lower Bound
unanswered
Upper Bound
unanswered
Intervention
Lower Bound
unanswered
Upper Bound
please answer, any body, any expert
did you get an answer?
Why not answer it yourself? This is from a free edX subject exam. If after 12 weeks you can't answer a few very easy questions, then what have you been doing? Obviously not the work.
Hi netspirit, can you answer these
Can you please answer problem no.2 of exploratory analysis( Using central limit theorem)
please help with the central limit theorem problem
what does the 22 seconds do in this question??? i found the upper and lower bound for the intervention but the control answers were incorrect. explain plz.
upper and lower bound answer plzzzz
To conduct a two-sample non-parametric test, we can use the Mann-Whitney U test. This test does not require any normality assumptions.
To calculate the p-value for the Mann-Whitney U test, you can follow these steps:
1. Rank all the cry time values from both groups combined. Assign the lowest value a rank of 1, the next lowest a rank of 2, and so on. If there are ties, assign the average rank to the tied values.
2. Calculate the sum of ranks for each group separately.
3. Calculate the U statistic for each group. The U statistic is the smaller of the two sums of ranks.
4. Use a table or software to find the critical value or p-value corresponding to the U statistic. The p-value is the probability of obtaining a value of U as extreme or more extreme than the observed U, assuming the null hypothesis is true.
In this case, we want to test whether the distribution of cry time is the same in both groups. The null hypothesis is that the distributions are the same, and the alternative hypothesis is that they are different. To determine the p-value, compare the calculated U statistic to the critical value or p-value from the table or software.
After obtaining the p-value, compare it to the significance level of 0.05. If the p-value is less than 0.05, reject the null hypothesis and conclude that there is evidence of a difference in the distributions of cry time between the two groups. If the p-value is greater than or equal to 0.05, fail to reject the null hypothesis and conclude that there is not enough evidence to suggest a difference in the distributions.
Now, concerning the exploratory analysis and the boxplot of cry time by group, you can plot a boxplot for each group separately. The boxplot will show you the median, quartiles, and any outliers for each group. To determine which group has more variability in cry time, look for a larger range or more spread-out whiskers on the boxplot. The group with a larger range or more spread-out whiskers will have more variability in cry time.
Moving on to constructing the 95% confidence interval for the average total cry time, we can use the central limit theorem to approximate the distribution of the sample mean. Given that the standard deviation of cry time within each group is known and equal to 22 seconds, we can use the formula for the confidence interval:
CI = x̄ ± z * (σ/√n)
Here, x̄ is the sample mean, z is the Z-value corresponding to the desired confidence level (e.g., 1.96 for a 95% confidence level), σ is the known standard deviation, and n is the sample size.
Calculate the confidence interval separately for the control group and intervention group using their respective sample means and the known standard deviation. The lower bound is the sample mean minus the margin of error and the upper bound is the sample mean plus the margin of error.
Remember that the central limit theorem assumes that the sample size is large enough (typically considered to be at least 30) for a valid approximation.