In: Math

# You have taken a random sample of 286 children in Virginia’s homeless shelters to establish their...

You have taken a random sample of 286 children in Virginia’s homeless shelters to establish their needs (using an establish Needs Scale). The mean is 5.32, the mode is 6, and the median is 6.
A. Provide a complete description of this sample (including shape and appropriate measures of center and spread).
B. Why did you choose the measure of center detailed above?
C. Regardless of 10b, why is a confidence interval of the mean a valid estimate of the mean?
D. Calculate and interpret a 95% confidence interval for the mean.
E. What is the population for this analysis?

## Solutions

##### Expert Solution

Ans A)

The sample size is 286 which is larger than 30 , and hence as per the central limit theorem this data can be considered to follow normal distribution. The mean value is 5.32 and median = 6 , this tells us that since the mean value < median value, the data is left skewed

Ans B)

Since the data is skewed to the left , for skewed data the measure of central tendency is the median value

Ans C)

Despite of the fact that the data is skewed, since the sample size is large, as per the central limit theorem we prefer to use the confidence interval of mean, because the data is considered to follow normal distribution

ANs d)

Since the sample consists of 286 chidren in virginia’ homeless shelters, the population under analysis are all the children who live in Virginia’s homeless shelters

For confidence interval the formula:

x bar - z* Standard error , x bar + z * standard error

thus for its calculation we need the value of standard error as well

x bar = mean of data = 5.32 , and z value for 95% c-level is 1.96

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