T.DIST.2T

Calculates the two-tailed Student’s t-distribution, commonly known as two-tailed t-distribution.

Syntax:

T.DIST.2T(x, deg_freedom)

x is required, and is the value that you want to use to evaluate the distribution.

deg_freedom is required, and is the degrees of freedom of the distribution.

Example:

If x contains 2.5 and deg_freedom contains 19:

T.DIST.2T(2.5, 19)

returns 0.021740411

x:

deg_freedom:

Result:

0.021740411

Application:

Let's imagine a scenario where a company, "TechGadgets Inc.," wants to test a new battery for their latest smartphone model. They claim that the new battery allows the phone to last for at least 24 hours on a single charge. As a quality control manager, you want to verify this claim.

The Hypothesis

Null Hypothesis (H0): The average battery life is equal to or greater than 24 hours. (μ≥24)
Alternative Hypothesis (Ha): The average battery life is less than 24 hours. (μ<24)

You decide to conduct a two-tailed t-test to determine if there's a statistically significant difference from their claim. You select a random sample of 15 smartphones and measure their battery life.

Data Collection

Here is the data from the sample of 15 smartphones:

	Sample	Battery Life (hours)
	A	B
1	1	23.5
2	2	24.1
3	3	23.8
4	4	24.5
5	5	23.9
6	6	23.6
7	7	24.2
8	8	23.7
9	9	24
10	10	23.3
11	11	24.3
12	12	23.8
13	13	24.4
14	14	23.9
15	15	24.1

Calculations

From this data, you calculate the following:

Sample Mean ( $\overset{x}{ˉ}$ ): 23.94 hours
Sample Standard Deviation (s): 0.35 hours
Sample Size (n): 15
Hypothesized Population Mean (μ0): 24 hours
Degrees of Freedom (df): n−1=15−1=14

The t-statistic

Next, you calculate the t-statistic using the formula:

$t = \frac{x ˉ - μ _{0}}{\frac{s}{n}}$

$t = \frac{23.94 - 24}{\frac{0.35}{15}}$

$t = \frac{- 0.06}{\frac{0.35}{3.873}}$

$t = \frac{- 0.06}{0.0904}$

$t \approx - 0.6637$

Using the T.DIST.2T Function

Now, you want to find the two-tailed probability (p-value) associated with this t-statistic. This is where the T.DIST.2T function is useful.

x: The absolute value of the t-statistic, which is 0.6637.
deg_freedom: The degrees of freedom, which is 14.

Using the function:

T.DIST.2T(0.6637, 14)

The function returns a p-value of approximately 0.51766.

Conclusion

With a p-value of 0.51766, which is much greater than the typical significance level of 0.05, we fail to reject the null hypothesis. This means there is not enough evidence to conclude that the average battery life is significantly different from 24 hours. The claim made by TechGadgets Inc. seems to be supported by the sample data.

Result for T.DIST.2T(0.6637, 14):

0.517663458