Applied Mathematics

Inferential Statistics

Easy

applied

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 :

1.85

$-2.05$

$-2.15$

1.65

✅ Correct Option: 4

$z = \frac{\bar{x} - \mu}{\sigma/\sqrt{n}} = \frac{20.55 - 20}{3/\sqrt{81}} = \frac{0.55}{1/3} = 1.65$ .

2023: 11 Aug Shift 1

A Simple random sample consists of four observation 1, 3, 5, 7. The point estimate of population standard deviation is

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Five students are selected at random from a school and their weights are found to be 50, 51, 53, 54 and 62. The point estimation of the population mean 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:

2023: 15 June Shift 2

Match List - I with List - II.

List - I	List - II
(A) A special characteristic of a population is called	(I) Sample Size
(B) The number of statistical individuals in a sample is called	(II) Statistic
(C) A special characteristic of a sample is called	(III) Standard error
(D) The standard deviation of the sampling distribution of a statistic is known as its	(IV) Parameter

Choose the correct answer from the options given below :

2023: 7 June Shift 1

T- test : A t- test is a test of difference for parameter data $t = \frac{\overline{x1} - \overline{x2}}{s\sqrt{\frac{1}{n1} + \frac{1}{n2}}}$

Then read the following statements and choose the correct statements

(A) the null hypothesis and the alternative hypothesis have the same viewpoint

(B) In t- test testing the significance of mean value is done, when sample size is small

(D) Testing is a process used by statisticians to accept or reject the hypothesis

(E) if the value of test statistics is greater than the table values, we do not reject the null hypothesis

Choose the correct answer from the options given below :

2026: 21 May Shift 2

Match the LIST-I with LIST-II

LIST-I (Term)		LIST-II (Definition)
A. Confidence level		I. In a confidence interval, the range of values, above and below the sample statistic.
B. Margin of error		II. It is the probability of making Type-I error, when null hypothesis is true as an equality.
C. Level of significance		III. It involves the use of sample data to calculate a single value of an unknown population parameter.
D. Point estimation		IV. It describes the uncertainty of a sampling method.

Choose the correct answer from the options given below:

Consider the following hypothesis test : H0:μ≤20H_0 : \mu \leq 20H0​:μ≤20 H1:μ>20H_1 : \mu > 20H1​:μ>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 :

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

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 :