Statistics & Applications

Inferential

Medium

applied

Which of the following are correct about t-test statistics?

(A) The mean of t-test distribution is 0.

(B) It depends on the degrees of freedom.

(C) It depends on population standard deviation.

(D) With more degrees of freedom, it closely resembles standard normal distribution.

Choose the correct answer from the options given below:

(A) and (B) only

(B), (C) and (D) only

(A), (B), (C) and (D)

(A), (B) and (D) only

✅ Correct Option: 4

(A) The mean of t-test distribution is 0.

The t-distribution is centered at zero, similar to the standard normal distribution. The distribution itself is balanced at 0.

(B) It depends on the degrees of freedom.

Degrees of freedom (df) = sample size - 1. Different df values create different t-distribution shapes.

Small df results in flatter, wider tails (more spread out).

Large df results in taller, thinner tails (more concentrated).

The df must be known to use the t-distribution.

The z-test uses population standard deviation ( $\sigma$ ) when $\sigma$ is known.

The t-test uses sample standard deviation ( $s$ ) when $\sigma$ is unknown.

The t-test is used precisely because the population standard deviation is unknown and must be estimated from the sample.

This statement is incorrect.

(D) With more degrees of freedom, it closely resembles standard normal distribution.

When df is small (like 5), the t-distribution has fat tails.

When df is large (like 30+), the t-distribution approximates the normal distribution.

At df $\approx$ 30 or more, the t-distribution closely resembles the normal distribution.

Correct statements: (A), (B), and (D)

The answer is Option 4.

2026: 21 May Shift 1

A sample of size 9 from a normal population with sample mean $\bar{X} = 15.8$ and population estimated standard deviation $\sigma = 3.21$ , then 99% confidence interval for population mean is : $(Use: t_8(0.01) = 3.335)$

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?

2026: 30 May Shift 2

If the average rainfall in a given area is 8 inches and the following table represents the average rainfall for four consecutive years, then the value of test statistic 't' is_____.

Year	year 1	year 2	Year 3	year 4
Rainfall (inches)	8	5	6	5

2025: 15 May Shift 2

In reference to the Inferential Statistics, which of the following is NOT correct?

2026: 19 May Shift 1

Tamanna was researching on problem of under-age workers at factories. She met a suitable child and interviewed him. He put her in contact with three another workers. Those three workers brought her in contact with ten other underage workers. This process of sampling is known as:

2025: 21 May Shift 1

Which of the following are correct?

(A) The probability curve in t-distribution is symmetric about the line t=0.

(B) t-axis is an asymptote of the curve.

(D) As the number of degrees of freedom increases, the t-distribution curve moves closer to the binomial distribution.

Choose the correct answer from the options given below:

Solution

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