Question

Question 8. For finding p-values, there are two approaches - bootstrap or use a distribution for the test statistic under the null hypothesis (like standard normal, T, Chi-Square, F). Using the distribution approach requires some assumptions (such as normality, or approximate normality, of the population distribution, large sample sizes, etc.)

For the following testing scenarios, write down the assumptions that are needed

a. Testing of equality of proportions between two categorical variables - p1 and p2.

Ho: p1 = p2 vs H1: p1 /= p2. Sample size n1 and n2

b. Testing for equality of proportions between three categorical variables using the Chi-Square Goodness of Fit approach

Ho: p1 = p2 = p3 vs H1: at least one pair of pi's is not the same. Sample sizes n1, n2, n3. Total sample size n = n1+n2+n3

a. Testing of equality of population means between three populations using the ANOVA table.

Ho: mu1 = m2 = mu3 vs H1: not all population means are the same Sample size n1, n2, n3

Answer 1

a. Testing of equality of proportions between two categorical variables - p1 and p2.

Ho: p1 = p2 vs H1: p1 /= p2. Sample size n1 and n2

The sampling method for each population is simple random sampling.
The samples are independent.
Each sample includes at least 10 successes and 10 failures.

b. Testing for equality of proportions between three categorical variables using the Chi-Square Goodness of Fit approach

Ho: p1 = p2 = p3 vs H1: at least one pair of pi's is not the same. Sample sizes n1, n2, n3. Total sample size n = n1+n2+n3

The sampling method is simple random sampling.

The variable under study is categorical.

The expected value of the number of sample observations in each level of the variable is at least 5.

c)

Testing of equality of population means between three populations using the ANOVA table.

Ho: mu1 = m2 = mu3 vs H1: not all population means are the same Sample size n1, n2, n3

Normality – That each sample is taken from a normally distributed population.
Sample independence – that each sample has been drawn independently of the other samples.
Variance Equality – That the variance of data in the different groups should be the same.

Please revert back in case of any doubt.

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