Applied Mathematics

Inferential Statistics

Medium

Consider the following hypothesis test : $H_0 : \mu \leq 24$ , $H_a : \mu > 24$

A sample of 64 provided a sample mean of 24.3 . The population standard deviation is 2. The value of the test statistic is :

1.2

2.1

1.3

-1.2

✅ Correct Option: 1

Test statistic $z = \frac{\bar{x} - \mu_0}{\sigma / \sqrt{n}} = \frac{24.3 - 24}{2/\sqrt{64}} = \frac{0.3}{2/8} = \frac{0.3}{0.25} = 1.2$ .

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:

2026: 14 May Shift 2

Match the LIST-I with LIST-II

	LIST-I		LIST-II
A.	Simple random sampling	I.	to get a team of 7 students with AI knowledge, selecting one of the students who will bring 6 more students.
B.	Stratified sampling	II.	Asking colleagues to complete a survey for research work
C.	Convenience sampling	III.	Selection of 100 employees from a company with 500 employees keeping gender balance in mind
D.	Snowball sampling	IV.	Selection of 50 guests randomly from a party

Choose the correct answer from the options given below:

2023: 7 June Shift 1

Which of the following is false about the central limit theorem

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

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:

2023: 7 June Shift 1

Which of the following is not a statistic ?

Consider the following hypothesis test : H0:μ≤24H_0 : \mu \leq 24H0​:μ≤24, Ha:μ>24H_a : \mu > 24Ha​:μ>24 A sample of 64 provided a sample mean of 24.3 . The population standard deviation is 2. The value of the test statistic is :