Question

Hypothesis Testing. Follow the description of the assignment below.

Think of a problem of your interest, set up H0 and Ha and conduct the hypothesis test.

Describe the research problem. Determine the level of significance – use the levels: α=0.1 ,α=0.05 or α=0.01.

Identify the target population and the population parameter of interest (μ or p; μ_1- μ_2 or p_1-p_2). Set up H0 and Ha.

Provide sample evidence: (1) Data source: a) primary sources i.e. survey, experiment, observation or b) secondary sources i.e. database/registry, census, internet portals etc.; (2) Sample properties: random, large or small sample; and (3) Sample data: sample size, sample mean(s) or sample proportion(s).

Define critical test statistic values (z or t-value). Calculate sample test-statistics and observed significance level (p-value).

Evaluate the sample evidence: (1) compare the critical values for rejection with sample statistics values and (2) compare observed significance level (p-value) with significance level (α).

Provide conclusion (whether you reject or do not reject H0) and interpret the results.

The assignments are subject to teacher assessment. Good projects... • ... are based on an original and meaningful research problem, and on representative and interesting sample evidence; • ...present a correctly conducted hypothesis testing procedure with a valid conclusion and well interpreted results; • ...are clear, and have a nice presentation (include images if relevant).

Answer 1

Answer:

Given that,

Hypothesis Testing.

Situation:

To determine whether the patients are responsive to a particular chemotherapeutic agent, colonies of cells are grown from each patient and then treated with an agent.

To compare two agents, two samples are prepared simultaneously, from each patient, one sample treated with each drug, and the number of colonies in the culture counted.

Question:

Do the two treatments have the same effect on colony formation:

The samples are:

A	B
252	254
227	260
181	343
167	246
83	98
35	67
20	86
18	61
12	20
6	12
5	3
23	16
23	11
12	1
7	2
2	0

Using independent sample t-test as the parametric test, we have:

The hypothesis being tested is:

H0: µ1 = µ2

H1: µ1 ≠ µ2

The output is:

A	B2
67.06	92.50	Mean
87.19	115.33	Standard deviation
16	16	n
	30	df
	-25.438	difference(A-B2)
	10,451.631	pooled variance
	102.233	pooled standard deviation
	0	Hypothesized difference
	-0.704	t
	0.4870	p-value (two-tailed)

Since the p-value (0.4870) is greater than the significance level(0.05), we cannot reject the null hypothesis.

Therefore, we can conclude that the two treatments have the same effect on colony formation.

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