The _________ basically states that the sample mean is consistent.

The . . . . . . . . basically states that the sample mean is consistent.

A

LAN

B

LLN

C

LWN

D

None of the mentioned

A researcher conduct a hypothesis test and observes values from sample mean and sample standard deviation when n = 25, that do not lead to rejection of null hypothesis. He calculates the p value as 0.0667. What will happen to the p value if he observes the same sample mean and standard deviation for a sample > 25?

A

Stay the same

B

Increase

C

Decrease

D

May increase or decrease

A set of sample of 20 places of mean annual rainfall were randomly selected from a normally distributed universe that has mean annual rainfall of 320 cm. The sample mean was recorded 250 cm with standard deviation of 150 cm. Which one of the following significance tests is correct for the selected samples ?

A

Z - test

B

X² - test

C

F - test

D

t - test

Which of the following is correct regarding the Charpy toughness test: P. The sample is held vertically as cantilever beam. Q. The sample is held horizontally as simply supported beam. R. The Notch in the sample faces the striking hammer. S. The Notch in the sample is opposite to the striking hammer.

A

P, R

B

P, S

C

Q, R

D

Q, S

A student was studying primate uterine thickness. She had 3 samples of uterine tissues. The thickness in mm for the samples are as follows: Sample A – 4 mm, Sample B – 10 mm, Sample C – 1 mm Given the knowledge of menstrual cycle in humans, what phases do you think each sample belongs to?

A

Sample A: Menstrual phase, Sample B: Follicular phase, Sample C: Luteal phase

B

Sample A: Proliferative phase, Sample B: Luteal phase, Sample C: Menstrual phase

C

Sample A: Secretory phase, Sample B: Menstrual phase, Sample C: Proliferative phase

D

Sample A: Menstrual phase, Sample B: Secretory phase, Sample C: Follicular phase

Which of the following statements are true with regards to the selection of a sample size? (i) The sample size (n) may be a fixed percentage of lot size (N). (ii) The sample size (n) may be kept constant irrespective of lot size (N). (iii) Sample size (n) can be selected at the personal whim of the inspector.

A

i only

B

i, ii only

C

i, ii, iii

D

i, iii only

In a test of differences between proportions, two samples are taken. In the first sample, a sample size of 100 shows 25 successes. In the second sample, a sample size of 80 shows 25 successes. What would be the value of B in this case?

A

$$\frac{{30}}{{100}} + \frac{{25}}{{80}}$$

B

$$\frac{{30}}{{100}} \times \frac{{25}}{{80}}$$

C

$$\frac{{30 + 25}}{{100}}$$

D

$$\frac{{30}}{{100}} + \frac{{25}}{{180}}$$

For the solution of a system of discretized equations with consistent approximations to be consistent, which of these conditions is necessary?

A

Boundedness

B

Stability

C

Convergence

D

Accuracy

Consider the following statements with respect to the Export Preparedness Index, 2020: 1. It was published by the NITI Aayog in partnership with the Institute of Competitiveness. 2. It examines the export ecosystem of Indian States and Union Territories. 3. Policy, Business Ecosystem, Export Ecosystem and Export Performance are the four pillars of the Export Preparedness Index. 4. Gujarat emerged as the top-performing State in the 'Coastal States' category, followed by Kerala and Tamil Nadu. 5. In the category of 'Landlocked States', Madhya Pradesh is the best-performing State. Among 'Himalayan States' and 'City-States' Himachal Pradesh and Delhi are the top-performing States respectively. Which of the above statements are true?

A

Only 1, 2 and 3

B

Only 2, 4 and 5

C

Only 2, 3 and 4

D

Only 1, 4 and 5

Match the items of List - II with the items of List - I and select the code of correct matching List - I List - II (a) Chi-square Test (i) Testing the significance of the differences of the mean values among more than two sample groups. (b) ANOVA (F-test) (ii) Testing the goodness of fit of a distribution (c) Z - test (iii) Testing the significance of the difference of the mean values between two large sized samples (d) t - test (iv) Testing the significance of the difference of the mean values between two small sized samples when population standard deviation is not available

A

(a) - (i), (b) - (ii), (c) - (iii), (d) - (iv)

B

(a) - (iv), (b) - (iii), (b) - (ii), (d) - (i)

C

(a) - (i), (b) - (ii), (c) - (iv), (d) - (iii)

D

(a) - (ii), (b) - (i), (c) - (iii), (d) - (iv)

The _________ basically states that the sample mean is consistent.

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