Question

Assignment 1
Choose any one variable of interest (e.g., cups of coffee) and collect data from two independent samples (e.g., men vs. women, children vs. adults, college students vs. non-college students, etc.) could make up the data.. of minimum size n=5 each. Complete the following:

1. Indicate whether your variable is continuous or discrete.
2. Indicate which scale of measurement your variable is categorized as (nominal, ordinal, interval, or ratio).
3. Calculate the mean, median, and mode for each sample.
4. Provide a conclusion sentence that describes the difference between these two samples based on the two means (e.g., “the sample of men consume more coffee on average compared to the sample of women”).

Answer 1

following ample data is for number of cups of coffee per day for mean and women

S.N.	men	women
1	6	4
2	5	3
3	6	3
4	4	2
5	5	1

(a)Indicate whether your variable is continuous or discrete.

This is discrete variable.A variable whose values are whole numbers (counts) is called discrete.

(b)Indicate which scale of measurement your variable is categorized as (nominal, ordinal, interval, or ratio).

It is an interval scale with the additional property that its zero position indicates the absence of the quantity being measured.

(c)Calculate the mean, median, and mode for each sample.

S.N.	men	women
1	6	4
2	5	3
3	6	3
4	4	2
5	5	1
mean	5.2	2.6
median	5	3
mode	6	3

Provide a conclusion sentence that describes the difference between these two samples based on the two means (e.g., “the sample of men consume more coffee on average compared to the sample of women”).

(d)

here we use t-test with

null hypothesis H0:mu1=mu2 and alternate hypothesis H1:mu1>mu2

statistic t=|(mean1-mean2)|/((s_p*(1/n1 +1/n2)^1/2) with df is n=n1+n2-2 and s_p²=((n1-1)s1²+(n2-1)s2²)/n

since one tailed p-value is less than typical alpha=0.05, so we reject H0 and conclude that men consume more coffee on average compared to the sample of women

t-Test: Two-Sample Assuming Equal Variances
	Variable 1	Variable 2
Mean	5.2	2.6
Variance	0.7	1.3
Observations	5	5
Pooled Variance	1
Hypothesized Mean Difference	0
df	8
t Stat	4.110961
P(T<=t) one-tail	0.001693
t Critical one-tail	1.859548
P(T<=t) two-tail	0.003386
t Critical two-tail	2.306004