Applied Mathematics

Inferential Statistics

Easy

applied

Consider the following hypothesis test :

$\mu_o : \mu \leq 26$

$\mu_a : \mu > 26$

A sample of 36 is provided with a sample mean of 25.75. The population standard deviation is 3. The value of the test statistic is :

1.5

$-0.5$

0.75

$-0.25$

✅ Correct Option: 2

Test statistic $z = \frac{\bar{x} - \mu_0}{\sigma/\sqrt{n}} = \frac{25.75 - 26}{3/\sqrt{36}} = \frac{-0.25}{0.5} = -0.5$ .

2023: 15 June Shift 2

Consider the following hypothesis test :

$H_0 : \mu \leq 20$

$H_1 : \mu > 20$

A sample of 81 produced a sample mean of 20.55. The population standard deviation is 3. The value of the test statistic is :

2026: 29 May Shift 2

Match the LIST-I with LIST-II

LIST-I		LIST-II
A.	The measurable characteristic of a population is called	I. Statistic
B.	The measurable characteristic of a sample is called	II. Confidence level
C.	The percentage of all possible samples that can be expected to include the true population parameter is called	III. Confidence interval
D.	A range that could be expected to contain the population parameter of interest is	IV. Parameter

Choose the correct answer from the options given below:

2026: 21 May Shift 2

In a survey question for a sample of 250 individuals, 100 students gave response 'good', 60 gave response 'average' and 90 students gave response as 'extra ordinary'. The point estimate of the proportion in the population who respond 'extra ordinary' is:

2023: 23 May Shift 3

In the formula for Z-test statistic $Z = \frac{\bar{x} - \mu_0}{\frac{\sigma}{\sqrt{n}}}$ , mark the incorrect statement.

2022: 25 May Shift 1

Match List I with List II

LIST I	LIST II
A. A special characteristic of a population is known as a:	I. statistic
B. A special characteristic of a sample is known as a:	II. Confidence interval
C. The uncertainty of a sampling process is expressed by:	III. Estimation
D. The process by which one makes the inferences about a population based on the information obtained from a sample is known as:	IV. Parameter

Choose the correct answer from the options given below:

2023: 23 May Shift 3

The following data is available for two independent sample:

	SAMPLE-1	SAMPLE-2
sample size	8	10
sample mean	191	199
sample standard deviation	10	12

Then the value of t-statistic is :

Consider the following hypothesis test : μo:μ≤26\mu_o : \mu \leq 26μo​:μ≤26 μa:μ>26\mu_a : \mu > 26μa​:μ>26 A sample of 36 is provided with a sample mean of 25.75. The population standard deviation is 3. The value of the test statistic is :

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

Consider the following hypothesis test :

$\mu_o : \mu \leq 26$

$\mu_a : \mu > 26$

A sample of 36 is provided with a sample mean of 25.75. The population standard deviation is 3. The value of the test statistic is :