If the variables in the problem are categorical variables then using z-procedures and t-procedures to estimate μ or proving an inequality related to  μ does not make sense

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If the variables in the problem are categorical variables then using z-procedures and t-procedures to estimate μ or proving an inequality related to  μ does not make sense. Recall that  μ is the population mean and the mean can only be calculated if the variable is quantitative (ie numbers).

Examples of problems with categorical variables (buckets/bins).

1. We want to find out if the there is a higher percent of pre-term births among African Americans as compared to Asian Americans and White Americans. Next 500 pre-term births are recorded. counts in each group are tabulated

The categorical variable here is "Racial Group": African Americans, Asian Americans, White Americans. (3 Bins/buckets) 

This problem requires a Chi-Squared hypothesis test

p _Af -percent (or proportion or fraction) of pre term births - African Americans

p _As -percent (or proportion or fraction) of pre term births - Asian Americans

p _W - percent (or proportion or fraction) of pre term births - White Americans

(Ho: There is no difference in the percentages/fractions)

Ho : p _Af = p_As = p _W =1/3

Ha: Ho is not true (This is always the null and alternative hypothesis in a Chi-squared hypothesis test)

2. We will find evidence that the occurrence of breast cancer is more among women with post-graduate degrees as compared women with Bachelor's degrees, Associate's degrees or high school diplomas. Next 1000 breast cancer diagnoses are recorded. Counts in each bucket are recorded.

The categorical variable here is "Level of Education": Post-Graduate Degree, Bachelor's Degree, Associate's Degree, High School Diploma (4 bins/buckets)

This problem requires a Chi-Squared hypothesis test

p _M -percent (or proportion or fraction) of breast cancer - Post Graduate

p _B -percent (or proportion or fraction) of breast cancer - Bachelors

p _A - percent (or proportion or fraction) of breast cancer - Associates

p H  - percent (or proportion or fraction) of breast cancer - High School 

(Ho- There is no difference in the percents/fractions)

Ho : p _M = p_B = p _A = p_H  = 1/4

Ha: Ho is not true (This is always the null and alternative hypothesis in a Chi-squared hypothesis test)

3. Is it true that women are at a higher risk of thyroid problems than men? More specifically 75% of the cases are women. Next 200 thyroid problem diagnoses are recorded and counts in each bucket are tabulated.

The categorical variable here is "Gender": Men, Women (2 bins/buckets)

This problem requires a Chi-Squared hypothesis test

p _M - percent (or proportion or fraction) of thyroid problems - Men

p F  - percent (or proportion or fraction) of thyroid problems - Female

Ho: p_M  = 1/4 ; p_F  = 3/4 OR Ho: p_M  = 25% ; p_F  = 75%

Ha: Ho is not true (This is always the null and alternative hypothesis in a Chi-squared hypothesis test)

 

Examples of problems with quantitative variables (measurements) 

1. We want to find evidence that the mean cholesterol measurement among women is greater than that of men.

This is a two sample hypothesis problem where we are comparing two means.

The quantitative variable is "Cholesterol Level"

2. Estimate the length of pregnancy among African American women.

This is a single sample confidence interval

The quantitative variable is "Length of Pregnancy"

3. The brand name drug cures cold symptoms faster than the generic drug. Both drugs are tested on a sample of volunteers at different times and results are tabulated. 

This is a matched pair hypothesis test.

The quantitative variable is " Length of Cold Symptoms"

Exercise 21.2 Gregor Mendel has been called the "father of genetics," having formulated laws of inheritance even before the function of DNA was discovered. In one famous experiment with peas, he crossed pure breeds of plants producing smooth peas and plants producing wrinkled peas. The first-generation peas were all smooth. In the second generation (F2), he obtained 5474 smooth-pea plants and 1850 wrinkled-pea plants. Do these data agree with the conclusion that F2 is made up of 75% dominant trait (in this case "smooth") and 25% recessive trait ("wrinkled")?

Is this a problem related to categorical variable or a quantitative variable? Enter upper case "C" for categorical and upper case "Q" for quantitative variable. ?

Which test is used in this problem? (Copy and paste from the above examples)

State the null and alternative hypotheses. Refer to the above examples to see how to write the hypotheses. Use "s" for smooth and "w" for wrinkled. ps, pw

Null Hypothesis: ?

Alternative Hypothesis: ?