Statistics & Applications

Inferential

Medium

applied

A random sample of size 16 has 53 as mean. The sum of the squares of the deviations taken from mean is 150. If the population mean is 56 then the value of t-test statistic is:

-3.79

-5.79

-4.79

-2.79

✅ Correct Option: 1

Given information:

Sample size: $n = 16$
Sample mean: $\bar{x} = 53$
Sum of squares of deviations from mean: $\sum(x_i - \bar{x})^2 = 150$
Population mean: $\mu = 56$

The sample variance is calculated using:

$s^2 = \frac{\sum(x_i - \bar{x})^2}{n-1}$

$s^2 = \frac{150}{16-1}$

$s^2 = \frac{150}{15}$

$s^2 = 10$

Therefore, the sample standard deviation is:

$s = \sqrt{10}$

The t-test statistic formula is:

$t = \frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}}$

Substituting the values:

$t = \frac{53 - 56}{\frac{\sqrt{10}}{\sqrt{16}}}$

$t = \frac{-3}{\frac{\sqrt{10}}{4}}$

$t = -3 \times \frac{4}{\sqrt{10}}$

$t = \frac{-12}{\sqrt{10}}$

$t = \frac{-12}{3.162}$

$t = -3.79$

Therefore, the value of the t-test statistic is $-3.79$ .

2025: 22 May Shift 1

Which one of the following statement is not correct?

2025: 26 May Shift 2

Match List-I with List-II

List-I	List-II
Terms	definition
(A) POPULATION	(I) Measurable characteristics of the population such as mean, variance, standard deviation etc. of population
(B) SAMPLE	(II) Measurable characteristics of the sample such as mean, variance, standard deviation etc. of a sample
(C) PARAMETER	(III) Finite set of statistical individuals drawn from a population for investigation.
(D) STATISTIC	(IV) Collection of objects having the same characteristics

Choose the correct answer from the options given below:

2025: 30 May Shift 2

In reference to Inferential Statistics, if $\bar{x}$ is a sample mean of random data $\{x_i\}_{i=1}^n$ and $n$ is the sample size, then the formula $\frac{1}{n-1}\sum_{i=0}^n(x_i - \bar{x})^2$ represents

2025: 27 May Shift 1

Consider the following hypothesis test.

$H_0: \mu \leq 12$

$H_a: \mu > 12$

If a sample of 25 is taken with sample mean 15 and a sample standard deviation of 6, then the value of t-test statistic is:

2026: 12 May Shift 2

If the sample size ( $n$ ) is 32 in testing of hypothesis by t-test, then the degree of freedom ( $\gamma$ ) is equal to :

2026: 18 May Shift 2

In a survey question for a sample of 340 people, 85 persons gave positive response, 145 people gave negative response and 110 people were neutral, gave no response. What is the point estimate of the proportion in the population who respond positive?

A random sample of size 16 has 53 as mean. The sum of the squares of the deviations taken from mean is 150. If the population mean is 56 then the value of t-test statistic is:

Solution

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