A survey is taken to estimate the mean annual family income for families living in public...

A survey is taken to estimate the mean annual family income for families living in public housing in Chicago. For a random sample of 29 families, the annual incomes (in hundreds of dollars) are as follows: 90 77 100 83 64 78 92 73 122 96 60 85 86 108 70 139 56 94 84 111 93 120 70 92 100 124 59 112 79 a. Construct a box plot of the incomes. What do you predict about the shape of the population distribution? Does this affect the possible inferences? b. Using software, find point estimates of the mean and standard deviation of the family incomes of all families living in public housing in Chicago. c. Obtain and interpret a 95% confidence interval for the population mean d. iv) A city alderman claims that the mean annual family income for families living in public housing in Chicago is less than $10,000. Is there statistical evidence from the data to support this claim? Explain why or why not. (Hint: use the result of part (iii)

Expert Solution

a. Construct a box plot of the incomes. What do you predict about the shape of the population distribution? Does this affect the possible inferences?

The population distribution is skewed-right. Yes, this affects the possible inferences because the normal distribution condition is violated.

b. Using software, find point estimates of the mean and standard deviation of the family incomes of all families living in public housing in Chicago.

mean	90.24
sample standard deviation	20.99

c. Obtain and interpret a 95% confidence interval for the population mean

The 95% confidence interval for the population mean is between 82.26 and 98.23.

We are 95% confident that the true population mean is between 82.26 and 98.23.

confidence interval 95.% lower	82.26
confidence interval 95.% upper	98.23
margin of error	7.99
t(df = 28)	2.048

d. iv) A city alderman claims that the mean annual family income for families living in public housing in Chicago is less than $10,000. Is there statistical evidence from the data to support this claim? Explain why or why not. (Hint: use the result of part (iii)

Since the confidence interval's upper limit is less than $10,000, we have statistical evidence from the data to support this claim.

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orchestra answered 1 year ago

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