Let us see about the topic is one tailed vs two tailed t test. Now we can first see about the two tailed, when the two tails of the sampling distribution of the **normal curve** are used, the relevant test is known as two – tailed test. The second one is the alternative
hypothesis H_{1}: µ_{1}≠ µ_{2} is taken in two – tailed test for H_{0}: µ_{1}=µ_{2} . when there only one tail of the sampling
distribution of the normal curve is used, the test is described as one tail test.

**One- Tailed Test:**

**Two Tailed Test:**

**Example 1:- using one tailed vs two tailed t test**

The average hourly wage of a sample of 150 workers in plant A was Rs. 2.56 with a S.D. of Rs. 1.08. the average wage of a sample of 200 workers in plant B was Rs.2.87 with a S.D of Rs. 1.28. we can applicant safely assume that the hourly wage paid by plant B are higher than those paid by plant A?

**Solution:**

Let x1 and x2 denotes the hourly wages paid to workers in plant A and plant B respectively

We set up

H_{0}: µ_{1}=µ_{2}

H_{1}: µ_{1}< µ_{2} (one – tailed)

L.O.S: α = 0.05

Test Statistic

Z = `(barx^1-barx^2)/(sqrt((s^1/(2n^1))+(s^2/(2n^2))))`

= `(2.56-2.87)/(sqrt((1.08)^2/150 + (1.28)^2/200))`

|Z|= 2.453

**Critical Value:**

The table value of Z at 5% level in case of one-tailed test is Z = 1.645

**Conclusion:**

Since |Z| > 1.645, H_{0} is rejected at 5% level

The hourly wage paid by plant B is higher than those paid by plant A.

I am planning to write more post on **Paired Samples T Test**, **binomial probability distribution**, Keep checking my blog.

**Example 2:- using one tailed vs two tailed t test**

Given that on the average 4% of insured men of age 65 die within a year and that 60 of a particular group of 1000 such men died within a year. We can this group be regarded as a representative sample.

**Solution:**

Null hypothesis H_{0}: p = 0.04

H_{1}: p ≠ 0.04

**Test Statistic:**

p’ = 60/ 1000

= 0.06

p=0.04

q = 0.96

z = `(0.06 - 0.04)/(sqrt((0.04 * 0.96)/(1000)))`

= `0.2/ (sqrt((0.004*0.96)))`

=3.2

**Conclusion:**

Since |Z| > 3, H_{0} is rejected.

The group chosen is not a representative sample.