Question

1. How do you know if a hypothesis test is testing the claim between 2 population proportions or 2 means?
2. How is the test statistic for a claim about 2 population means, independent samples, standard deviations unknown, similar to the test statistic for 1 population mean, standard deviation unknown?
3. If the difference between the 2 population means is not significant, which means the test statistic falls within the "usual" area of the distribution, what is the decision about the null hypothesis?
4. How do you know if a hypothesis test is about independent or dependent samples?

Answer 1

A. Test of two proportion test is done when the following conditions are met :

i. The sampling method for each population is simple random sampling.

ii. The samples are independent.

iii. Each sample includes at least 10 successes and 10 failures.

iv. Each population is at least 20 times as big as its sample.

B. A hypothesis test on two population mean is done when :

is appropriate when the following conditions are met:

i. The sampling method for each sample is simple random sampling.

ii. The samples are independent.

iii. Each population is at least 20 times larger than its respective sample.

iv. The sampling distribution is approximately normal, which is generally the case if any of the following conditions apply :

i. The population distribution is normal.

ii. The population data are symmetric, unimodal, without outliers, and the sample size is 15 or less.

iii. The population data are slightly skewed, unimodal, without outliers, and the sample size is 16 to 40.

iv. The sample size is greater than 40, without outliers.

C. Test statistic for a claim about 2 population means, independent samples, standard deviations unknown, similar to the test statistic for 1 population mean, standard deviation unknown is a statistic of 2 sample t which is defined as follows :

t = [ (x1bar - x2bar) - d ] / SE

where x1bar is the mean of sample 1, x2bar is the mean of sample 2, d is the hypothesized difference between population means, and SE is the standard error.

And SE = sqrt[ (s1²/n1) + (s2²/n2) ]

Where s1² and s2² are variances of sample 1 and sample 2.

The hypothesis for above statistic is :

μ1 - μ2 = d μ1 - μ2 ≠ d (2 tailed)

Or μ1 - μ2 > d μ1 - μ2 < d (1 tailed)

Or μ1 - μ2 < d μ1 - μ2 > d

D. If the difference between the 2 population means is not significant, which means the test statistic falls within the "usual" area of the distribution, the decision about the null hypothesis is : accept the null hypothesis and conclude there is no significant difference in the means of the two groups.

E. If the values in one sample affect the values in the other sample, then the samples are dependent. If the values in one sample reveal no information about those of the other sample, then the samples are independent.

Ex : 2 sample t test is an example of independent sample test as the two population under consideration are independent of each other. Whereas paired t test is an example of dependent sample t test as it relates two depended group (marks of students before improvement of study habits and after improvement of study habits.)