PBHE 520 lab assignment 3

Part 1: Preliminary Report 1 DUE WEEK 3 – No Grade Given – Pass/Fail – OPTIONAL – NO LATE ASSIGNMENTS ACCEPTED

 

(i) Describe the household data using the appropriate descriptive statistics technique for each variable.  Hint: Calculate the mean, median, mode, proportion, range, and standard deviation, etc. as appropriate.

 

Table 1 contains the descriptive statistics for all the quantitative variables present in the data.

 

Descriptive statistics
  Annual Household Income Home Price No. Bedrooms Household Size
Count 100 100 100 100
Mean 131.313 289.991 3.18 3.63
Variance 655.021 1,261.221 0.77 1.81
Standard Deviation 25.593 35.514 0.88 1.35
Minimum 72.4 210.3 2.00 1.00
Maximum 261.75 381.5 5.67 7.00
Range 189.35 171.2 3.67 6.00
1st quartile 118.813 271.300 2.50 3.00
Median 131.350 287.300 3.00 3.50
3rd quartile 141.675 306.900 4.00 4.25
Interquartile Range 22.863 35.600 1.50 1.25
Mode 138.100 301.600 2.50 3.00

 

Table 1

 

The mean annual household income is $131.313, mean home price is $289.991, mean number of bedrooms is 3.18, and mean household size is 3.63.

The median annual household income is $131.350, median home price is $287.300, median number of bedrooms is 3.00, and median household size is 3.50.

The standard deviation of annual household incomes is $25.593, standard deviation of home prices is $35.514, standard deviation of number of bedrooms is 0.88, and standard deviation of household sizes is 1.35.

 

 

Table 2 contains the frequency and relative frequency distributions of all the qualitative variables present in the data.

 

Race Frequency Relative frequency
Black 29 29.0%
Hispanic 21 21.0%
White 50 50.0%
Grand Total 100 1.00
Had Heart Disease? Frequency Relative frequency
No 42 42.0%
Yes 58 58.0%
Grand Total 100 1.00

 

Table 2

 

Overall in the population, 29% are Blacks, 21% are Hispanics, and 50% are Whites.

Among the individuals in the population 42% did not have heart disease earlier and 58% had a heart disease.

 

(ii) Construct a frequency table and histogram of household income in increments of $50,000 (for example, $0–$50,000, $50,001–$100,000, $100,001-$150,000, and so on).

Table 3 contains the frequency table of household income in increments of $50,000.

Frequency Distribution – Annual Household Income
             
lower upper midpoint width frequency percent
0 < 50 25 50 0 0.0
50 < 100 75 50 10 10.0
100 < 150 125 50 76 76.0
150 < 200 175 50 12 12.0
200 < 250 225 50 1 1.0
250 < 300 275 50 1 1.0
100   100.0  

Table 3

Figure 1 contains the frequency histogram of household income in increments of $50,000.

 

Figure 1

 

 

Part 2: Preliminary Report 2 DUE WEEK 5 – No Grade Given – Pass/Fail – OPTIONAL

NO LATE ASSIGNMENTS ACCEPTED

You have already compute sample parameters for the data.

(i)  Test the hypotheses that the average household income in the township is greater than $100,000. Hint: Start by stating the null and alternative hypotheses.

 

 

 

(ii) Construct a 95% CI for the proportion of households with family history of heart disease, separately for each race.  Would you say the proportion of households with history of heart disease differ by race?

 

Table 4 contains the race wise proportions of having heart disease.

 

Race Had Heart Disease Grand Total
No Yes
Black 9 (31%) 20 (69%) 29
Hispanic 7 (33%) 14 (67%) 21
White 26 (52%) 24 (48%) 50
Grand Total 42 (42%) 58 (58%) 100

 

Table 4

 

 

 

 

 

Race Sample Proportion Sample Size 95% CI
Lower Limit Upper Limit
Black 0.69 29 0.52 0.86
Hispanic 0.67 21 0.47 0.87
White 0.48 50 0.34 0.62

 

Table 5

 

Table 5 contains the 95% CI for the proportion of households with family history of heart disease, separately for each race. The proportion of households with history of heart disease is same for all the races Black, Hispanic and White.

 

Part 3: Final Report DUE WEEK 7

You believe that income distribution differ by race.

(i) Formulate the null and alternative hypotheses you would use to for the test this claim.

 

 

(ii) Conduct the test and appropriately accept or reject your null hypotheses using ANOVA.

 

Table 6 contains the results of one-way ANOVA performed on annual household incomes by the variable race.

 

 

Anova: Single Factor
SUMMARY
Groups Count Sum Average Variance
Black 29 3794.75 130.853 803.700
Hispanic 21 2782.35 132.493 523.546
White 50 6554.2 131.084 649.685
ANOVA
Source of Variation SS df MS F P-value F crit
Between Groups 37.98 2 18.99 0.028 0.9720 3.090
Within Groups 64809.09 97 668.13
Total 64847.07 99

 

Table 6

 

(iii) Is there any statistically significant difference in the average household income based on race?

 

Table 6 contains the test statistic F (2, 97) = 0.028, p > 0.95. It indicates that data provides insufficient evidence to support the claim that there is a statistically significant difference in the average household income based on race.

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