t-test (independent sample)

An investigation was conducted to find out the effect of water concentration on the amount of oxygen released by hydrilla in a given time. The following data were gathered. 

Table A. Number of oxgen bubbles

Test Tube	Distilled water	Tap water
1	21	19
2	20	18
3	18	17
4	17	19
5	18	20
6	18	20
7	19	20
8	15	21
9	22	29
10	17	21

Here are the steps done to statistically treat the data above:

a. Hypotheses:

Null Hypothesis: X_{distilled water} = X_{tap water}

Alternative: X_{distilled water} ≠ X_{tap water}

b. Significance level: .05

c. Results

Group Statistics

number of oxygen bubbles	type of water	N	Mean	Std. Deviation	Std. Error Mean
	distilled water	10	18.5000	2.06828	.65405
	tap water	10	20.4000	3.27278	1.03494

Independent Samples Test

number of oxygen bubbles	t-test for Equality of Means
	t	df	Sig. (2-tailed)	Mean Difference	Std. Error Difference	95% Confidence Interval of the Difference
	-1.552	18	.138	-1.9000	1.22429	Lower	Upper
						-4.47214	.67214

 The t -vale of -1.552, with degree of freedom of 18 has a significance level of .138, which is greater than the significance level of .05. 

Therefore the null hypothesis is rejected.

t - test (paired sample)

A study was conducted to find out the effect of temperature on the height of spring onion variety X. The following data were collected.

Table A. Height (cm) of Spring Onion Variety X

Plant No.	20 deg. Celsius	30 deg. Celsius
1	45.3	32
2	45	32.1
3	47	36.8
4	46	35
5	45	31
6	46.3	29.8
7	48	32
8	44.9	33.5
9	42	34.2
10	43.8	33

Null Hypothesis: There is no significant difference between the mean of the height of variety X at 20 and 30 degrees Celsius.

Findings: 

Table 1: Paired Samples Statistics

	Mean	N	Std. Deviation
height @ 20 deg C	45.3300	10	1.67136
height @ 30 deg C	32.9400	10	2.03153

Table 2: Paired Samples Test

height @ 20 deg C - height @ 30 deg C	t	df	Sig. (2-tailed)
	14.589	9	.000

Analysis, Interpretations and Conclusions: 

Table 1 shows the means of 45.33 cm and 32.94 cm as heights of variety X at 20 and 30 deg. C respectively, with corresponding SD of 1.67 and 2.03. 

Table 2 presents a t - value of 14.589 with 9 as degree of freedom. The t - value having a significance level of .000 is significant. 

Reject the null hypothesis; there is a significant difference in the height of variety X at 20 and 30 deg. C.

t - test

A research was conducted to find out the effect of plant extract X concentration as mosquito larvicide. The following data were gathered. 

Table A: Mortality of larvae within 24 h

Dishes	20% extract	50% extract
1	17	15
2	18	18
3	17	19
4	15	19
5	19	20
6	20	18
7	18	17
8	18	15
9	19	18
10	17	17

Hypotheses:

H₀ : Mean of Mortality in 20% extract = Mean of Mortality in 50% extract

H₁:  Mean of Mortality in 20% extract ≠ Mean of Mortality in 50% extract


Level of Significance: 0.05

Solving for T value (Results given)

Table 1. Group Statistics

larvae mortality	extract concentration	N	Mean	Std. Deviation
	20% extract	10	17.8000	1.39841
	50% extract	10	17.6000	1.64655

Table 2. Independent Samples Test

larvae mortality	Sig.	t-test for Equality of Means t	df		Mean Difference	Std. Error Difference
	.561	.293	18		.2000	.68313

Table 1 shows the group statistics of the scores obtained. It can be seen that the mean mortality are 17.8 and 17.6 in 20% and 50% extracts, respectively.

Table 2 shows the results of independent sample t-test.  the t - value of 0.293 having a significance level of .561 is not significant, at df = 18.

Conclusion: Uphold the null hypothesis,

H₀ : Mean of Mortality in 20% extract = Mean of Mortality in 50% extract.

(If the t-value has a significance level lower than .05, the null hypothesis will be rejected. In this particular example, the significance level of the t-value is .561, so the null hypothesis is accepted.)