Applied Mathematics

Inferential Statistics

Hard

applied

For testing the difference between the means of two samples, the following data is available :

Size Mean Variance
Sample 1 5 40 101
Sample 2 7 30 60

The value of the t-statistics is :

	Size	Mean	Variance
Sample 1	5	40	101
Sample 2	7	30	60

$10\sqrt{\frac{7}{222}}$

$20\sqrt{\frac{7}{222}}$

$5\sqrt{\frac{7}{222}}$

$\sqrt{\frac{7}{222}}$

✅ Correct Option: 1

Pooled variance $S_p^2=\frac{n_1 s_1^2+n_2 s_2^2}{n_1+n_2-2}=\frac{505+420}{10}=92.5=\frac{185}{2}$ .

$t=\frac{\bar{x_1}-\bar{x_2}}{\sqrt{S_p^2(1/n_1+1/n_2)}}=\frac{10}{\sqrt{92.5\cdot 12/35}}=\frac{10}{\sqrt{222/7}}=10\sqrt{\frac{7}{222}}$ .

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 :

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:

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: 23 May Shift 3

A simple random sample consists of three observations 1, 3, 5. The point estimate of the population standard deviation is :

2026: 21 May Shift 2

Statistical inference is a process through which inference about the population are made based on informations obtained from the:

2026: 29 May Shift 2

Consider the following hypothesis test:

$H_0: \mu \leq 35$

$H_a: \mu > 35$

A sample of 25 provided a sample mean of 34.65. The population standard deviation is 4. The value of the t-test statistic is

For testing the difference between the means of two samples, the following data is available : SizeMeanVarianceSample 1540101Sample 273060 The value of the t-statistics is :

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

For testing the difference between the means of two samples, the following data is available :

Size Mean Variance
Sample 1 5 40 101
Sample 2 7 30 60

The value of the t-statistics is :