Statistics & Applications

Inferential

Medium

applied

Consider the following hypothesis test,

$H_0: \mu = 15$

$H_a: \mu ≠ 15$

A sample of 50 provided a sample mean of 14.15. If the sample standard deviation is 3, then the value of the test statistic t0-test is

-1

-2

✅ Correct Option: 2

Given information:

Hypothesized mean $\mu_0 = 15$

Sample mean $\bar{x} = 14.15$

Sample standard deviation $s = 3$

Sample size $n = 50$

The t-test statistic formula:

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

Calculate the standard error:

$\text{Standard Error} = \frac{s}{\sqrt{n}}$

$= \frac{3}{\sqrt{50}}$

$= \frac{3}{7.071}$

$\approx 0.424$

Calculate the numerator:

$\bar{x} - \mu_0 = 14.15 - 15$

$= -0.85$

Calculate the t-statistic:

$t = \frac{-0.85}{0.424}$

$= -2.00$

The test statistic value is $|t| = 2$ .

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:

2026: 15 May Shift 1

The central limit theorem states that the sampling distribution of the sample mean approaches the 'X' distribution, as the sample size gets larger, no matter what the shape of the population is, then 'X' is

2026: 18 May Shift 2

The monthly salaries of workers in a garment factory are normally distributed. The mean salary is ₹ 10,000 and standard deviation is ₹ 625. If 2,500 workers are getting salary less than ₹ 10,000, then the total number of workers in the factory is:

2026: 22 May Shift 2

A company has been producing steel tubes of mean inner diameter of 3 cm. A sample of 17 tubes gives an inner diameter of 3.01 cm and a standard deviation of 0.064. Then the value of the t-test statistic is:

2026: 18 May Shift 2

Match the LIST-I with LIST-II

LIST-I	LIST-II
A. Confidence interval	I. Sampling distribution of the sample mean approaches normal distribution as the sample size gets larger, no matter what the shape of the population distribution is.
B. Hypothesis	II. A measurable characteristic of a sample.
C. Central limit theorem	III. The amount of uncertainity associated with a sample estimate of a population parameter.
D. Statistic	IV. An educated guess which needs to be tested.

Choose the correct answer from the options given below:

2026: 21 May Shift 1

As per the concept of inferential statistics, population stands for:-

Consider the following hypothesis test, H0:μ=15H_0: \mu = 15H0​:μ=15 Ha:μ≠15H_a: \mu ≠ 15Ha​:μ=15 A sample of 50 provided a sample mean of 14.15. If the sample standard deviation is 3, then the value of the test statistic t0-test is

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CUET Mathematics Past Year Questions (Topic-Wise)

Consider the following hypothesis test,

$H_0: \mu = 15$

$H_a: \mu ≠ 15$

A sample of 50 provided a sample mean of 14.15. If the sample standard deviation is 3, then the value of the test statistic t0-test is