Statistics & Applications

Inferential

Medium

applied

Consider the following test:

H₀: μ ≤ 12

H₁: μ > 12

A sample of 36 provided a sample mean $\bar{x} = 16$ and a sample standard deviation S=4.2. Then the value of the t- test statistic is:

5.32

2.67

34.26

5.71

✅ Correct Option: 4

Given information:

Sample size $n = 36$

Sample mean $\bar{x} = 16$

Sample standard deviation $s = 4.2$

Hypothesized mean $\mu_0 = 12$ (from $H_0: \mu \leq 12$ )

The t-test statistic formula is:

$t = \dfrac{\bar{x} - \mu_0}{s/\sqrt{n}}$

Calculate the standard error $s/\sqrt{n}$ :

$\sqrt{n} = \sqrt{36}$

$\sqrt{n} = 6$

$\dfrac{s}{\sqrt{n}} = \dfrac{4.2}{6}$

$\dfrac{s}{\sqrt{n}} = 0.7$

Calculate the t-statistic:

$t = \dfrac{16 - 12}{0.7}$

$t = \dfrac{4}{0.7}$

$t = 5.71$

Therefore, the value of the t-test statistic is $5.71$ .

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Consider the following test: H₀: μ ≤ 12 H₁: μ > 12 A sample of 36 provided a sample mean xˉ=16\bar{x} = 16xˉ=16 and a sample standard deviation S=4.2. Then the value of the t- test statistic is:

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

Consider the following test:

H₀: μ ≤ 12

H₁: μ > 12

A sample of 36 provided a sample mean $\bar{x} = 16$ and a sample standard deviation S=4.2. Then the value of the t- test statistic is: