7. In 2015, the Census Bureau reported that 20% of all Maryland households had i

Question

7. In 2015, the Census Bureau reported that 20% of all Maryland households had income above $100,000. During that same year, in a survey of 400 randomly selected Montgomery County households, 100 had income above s100,000. Do the data provide sufficient evidence to conclude that the proportion of all Montgomery County households with income above s100,000 is greater than 20 the proportion of all Maryland households with income above S100,000. a. Using proper notation define the parameter and state the hypotheses for testing if this sample provides evidence that the proportion of Montgomery County households with income above S100,000 is greater than 0.20, of all Maryland households with income above $100,000. b. Calculate the observed sample statistic. Use proper notation. c. Describe how you would generate a single randomization sample in this situation, and identify the statistic you would record for each sample. d. Use the provided randomization distribution (based on 100 samples) to estimate the p-value for this sample. 0.18 0.24

Explanation / Answer

Hypothesis Testing -

Hypotheses are :

H0 : proportion of persons (p) earning above $100000 is equal to .2 ( p = .2)

Ha : proportion of persons(p) earning above $100000 is greater than .2 ( p > .2 )

Test statistic value is calculated as : ( p^ - p ) / ( p^ . (1-p^ ) / n ) where p^ = .25 and n = 400

= 2.31

P-value is calculated as P (Z > 2.31 ) ( It is a one tailed test )

Using normal distribution tables we get P-value equals

This is a type 2 error as null hypothesis is true ( proportions are same ) and null is rejected as p-value is less than .05 so rejecting null hypothesis when it is true is a type 1 error.

TY!

0.01044 which is less than .05 and hence null hypothesis is rejected at 5% level of significance and thus proportion is greater than .2

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