Statistics & Applications

Inferential

Medium

applied

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 $\alpha = 0.05$ )

(23, 25)

(22.2, 27.8)

(22.8, 27.2)

(23.2, 28.8)

✅ Correct Option: 2

Standard error $=\dfrac{10}{\sqrt{49}}=\dfrac{10}{7}$ .

Margin of error $=1.96\times\dfrac{10}{7}=2.8$ .

Interval $=25\pm 2.8=(22.2,\,27.8)$ .

2026: 31 May Shift 2

Consider the following hypothesis test :

$H_0: \mu \le 35$

$H_a: \mu > 35$

A sample of 49 provided a sample mean of 38.2 The population standard deviation is 8. The value of test-statistic is,

2025: 19 May Shift 1

Which of the following are types of "statistical inferences"?

(A) Point estimation

(B) Interval estimation

(D) Hypothesis testing

Choose the correct answer from the options given below:

2025: 21 May Shift 1

Consider the following hypothesis test,

$H_0: \mu = 15$

$H_a: \mu ≠ 15$

A sample of 50 provided a sample mean of 14.15. If the sample standard deviation is 3, then the value of the test statistic t0-test is

2026: 19 May Shift 2

Match the LIST-I with LIST-II

	LIST-I		LIST-II
A.	Population	I.	A subgroup of members of the population.
B.	Sample	II.	The measurable characteristic of population.
C.	Parameter	III.	The measurable characteristic of sample.
D.	Statistic	IV.	A collection of all elements having same characteristic.

Choose the correct answer from the options given below:

2025: 3 June Shift 2

The following data are from a random sample: 5,8,10,7,10,14, then the point estimate of the population standard deviation is

2025: 2 June Shift 1

If $x_1, x_2, x_3, ..., x_n$ are n observations in a sample then which of following is/are TRUE?

(A) The mean $\bar{x}$ has n degree of freedom

(B) The mean $\bar{x}$ has (n-1) degree of freedom

(D) The standard deviation of the sample has n degree of freedom

Choose the correct answer from the options given below:

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 zα/2=1.96z_{\alpha/2} = 1.96zα/2​=1.96 where α=0.05\alpha = 0.05α=0.05)