Applied Mathematics

Inferential Statistics

Easy

applied

From a population having a mean of 20 and standard deviation 2, a random sample of size 64 is taken and its mean is found to be 19.5. The test statistic to test that the sample is taken from the population is

$-2$

$-0.5$

$0.25$

✅ Correct Option: 2

Test statistic: $z = \frac{\bar{x} - \mu}{\sigma/\sqrt{n}} = \frac{19.5 - 20}{2/\sqrt{64}} = \frac{-0.5}{0.25} = -2$ .

2023: 15 June Shift 2

A simple random sample consists of four observations 7, 8, 10, 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: 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 :

2023: 7 June Shift 1

Which of the following is false about the central limit theorem

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: 30 May Shift 3

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 :

Solution