final lab assignment for pbhe520 biostatistics

We were presented with an excel sheet of data and was asked to analyze it according to three different parts over seven weeks.  The purpose of this analysis is to determine several factors which are marked by bold faced print throughout the report.  The following is my attempt at this analization.

Part 1: Due Week 3

I was asked to use the surveyed data to figure all of the data needed.

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

Race:    See Appendix 1

Info:

Mean Annual household income- $131.313

Mean Home price-$298, 991

Mean No of bedrooms-3.18

Mean household size 3.63

Standard deviation of annual household income is $25,593

Standard deviation of home price-$35,514

Standard deviation on No of Bedrooms-0.88

Standard deviation for household size is 1.35

Heart Disease:

Had Heart Disease Frequency Relative Frequency
No 42 42%
Yes 58 58%
Grand Total 100 1.00

Section 2-Frequency Chart See attachment in excel (I was unable to copy and paste this into the assignment)

Part 2: Due Week 5

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

The null and alternative hypothesis are:

H0: The average household income of the township is equal to $100,000: U=100.
Ha: The average household income in the township is greater than $100,000 : u>100

I chose a=0.05 as my level of significance

Since n>30, use z-test for the single mean.  The critical value for this right tailed test is 1.645.

The rejection region for this test is z>1.645.

( 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?

Race Had Heart Disease Grand Total
No Yes
Black 9 20 29
Hispanic 7 14 21
Caucasian 26 24 50
Grand Total 42 58 100

The 95% CI for the following households for family history of heart disease are as follows:

Black: Sample proportion-0.69, sample size-29, lower limit-0.52, upper limit-0.86

Hispanic: sample proportion-0.67, sample size-2, lower limit-0.47, upper limit-0.87

White: sample proportion-0.48, sample size-50, lower limit-0.34, upper limit-0.62

The proportion of households is the same for all three races.

Part 3: Due week 7

You believe the income differ by race.

  • Formulate the null and alternative hypothesis you would use for this claim.

The Null & alternative hypothesis are as follows:

H0: There is no significant difference between income and distributions by race; u1=u2=u3.
Ha: The income distributions differ by race

  • Conduct the test and appropriately accept or reject your null hypothesis using ANOVA

I chose a=0.05 as the level of significance:

ANOVA-single factor

Summary:

Race count sum average Varience
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
  • Is there any statistical significant difference in the average household income based on race?

The table above contains the test statistic F (2,97)=0.028, p>0.95.  This data, unfortunately, provides insufficient evidence to support the claim that there is a difference in household income by race.

References:

Gerstman, B. Burt. (2008). Basic biostatistics for public health practice. Boston, Toronto, London, Singapore. Jones and Bartlett publishers.

Stat Trek. (n.d.). What is hypothesis testing? Retrieved from www.statrek.com

Pezzullo, John. (2013). Biostatistics for dummies. Hoboken, New Jersey.  John Wiley and Sons Publishing.

Boonshoft School of Medicine. (n.d.) Principles of biostatistics or medicine. Power point presentation. Retrieved from https://www.medwright.edu.

Appendix 1 Race  Use pie chart for this.

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