Statistics & Applications

Inferential

Medium

applied

A company has been producing steel tubes of mean inner diameter of 2 cm. A sample of 10 tubes gives an inner diameter of 2.01 cm and a variance of 0.0004 cm². The value of test statistic is :

2.5

1.5

2.36

0.512

✅ Correct Option: 2

Given information:

Population mean (μ) = 2 cm
Sample size (n) = 10 tubes
Sample mean (x̄) = 2.01 cm
Sample variance (s²) = 0.0004 cm²

The sample standard deviation is needed for the test statistic formula.

$s = \sqrt{s^2}$

$s = \sqrt{0.0004}$

$s = 0.02$ cm

For a small sample size without known population standard deviation, the t-test statistic is used:

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

Substituting the values:

$t = \frac{2.01 - 2.00}{0.02/\sqrt{10}}$

$t = \frac{0.01}{0.02/\sqrt{10}}$

$t = \frac{0.01}{0.02/3.162}$

$t = \frac{0.01}{0.006325}$

$t = 1.58$

$t \approx 1.5$

Therefore, the value of the test statistic is 1.5.

2024: 16 May Shift 1

The following data is from a simple random sample :

$15,23, x, 37,19,32$

If the point estimate of the population mean is $23$ , then the value of $x$ is :

2026: 25 May Shift 1

A simple random sample of 49 items from a population with standard deviation 10 resulted in a sample mean of 25. Then the 95% confidence interval for population mean are :

(Given $z_{\alpha/2} = 1.96$ where $\alpha = 0.05$ )

2026: 12 May Shift 2

The following data are from a simple random sample: 3, 6, 8, 15, 5, 11. What is the point estimate of the population mean?

2025: 30 May Shift 1

Match List-I with List-II

List-I	List-II
(A) The chance of observing a specific outcome in an experiment	(I) Parameter
(B) A method used to estimate the population parameters	(II) Estimation
(C) A value that describes an entire population	(III) Statistic
(D) A measurable characteristic of a sample	(IV) Probability distribution

Choose the correct answer from the options given below:

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: 27 May Shift 1

Consider the following hypothesis test:

$H_0: \mu \leq 3432$

$H_a: \mu > 3432$

A sample of 96 provided a sample mean $\bar{x} = 3648$ and sample standard deviation $s=802$ then the degree of freedom of t-distribution is:

A company has been producing steel tubes of mean inner diameter of 2 cm. A sample of 10 tubes gives an inner diameter of 2.01 cm and a variance of 0.0004 cm². The value of test statistic is :

Solution

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