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In reference to Inferential Statistics, if $\bar{x}$ is a sample mean of random data $\{x_i\}_{i=1}^n$ and $n$ is the sample size, then the formula $\frac{1}{n-1}\sum_{i=0}^n(x_i - \bar{x})^2$ represents

Match List-I with List-II

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A random sample of 100 individuals provides 25 positive responses.

Then the point estimate of the population proportion with "positive" responses is:

Match List-I with List-II

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In a survey for a sample of 300 individuals, 180 persons gave responses 'Yes' and 100 gave responses 'No' and 20 gave "No response". Then point estimate of proposition in the population who responded "Yes" is

In reference to Inferential Statistics, for 20 degrees of freedom, the least statistical t-value among the given below is:

If a sample has 'n' observation $x_1$, $x_2$ ............. $x_n$ with 'm' constraints on these values then degree of freedom of sample statistic is:

A 95% confidence interval for a population mean was reported to be 152 to 160. If standard deviation $\sigma = 15$ . Then the sample size is : ($Z_{0.025}$=1.96)

Consider the following hypothesis test:-

H₀: μ = 20

H₁: μ ≠ 20

A sample of 40 provided a sample mean of 19. The standard deviation is 3. Then the value of the t-test statistic is:

Consider the following hypothesis test:

$H_0: \mu \leq 3432$

$H_a: \mu > 3432$

A sample of 96 provided a sample mean $\bar{x} = 3648$ and sample standard deviation $s=802$ then the degree of freedom of t-distribution is:

In a survey question for a sample of 250 individuals, 120 persons gave response 'yes', 80 persons gave response 'no' and 50 gave 'no response'. The point estimate of the proportion in the population who responded 'yes' is:

Consider the following hypothesis test.

$H_0: \mu \leq 12$

$H_a: \mu > 12$

If a sample of 25 is taken with sample mean 15 and a sample standard deviation of 6, then the value of t-test statistic is:

Match List-I with List-II

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With reference to sampling, which of the following are correct?

(A) Simple random sampling is probability sampling

(B) Snow-ball sampling is non-probability sampling

(C) Stratified sampling is probability sampling

(D) Cluster sampling is non-probability sampling

Choose the correct answer from the options given below:

The point estimate of the population standard deviation as per the below mentioned data from a simple random sample 6,10,15,12,9,8 will be :-

Consider the following test:

H₀: μ ≤ 12

H₁: μ > 12

A sample of 36 provided a sample mean $\bar{x} = 16$ and a sample standard deviation S=4.2. Then the value of the t- test statistic is:

Rajesh calculated 95% confidence level. What does he mean by that?

(A) He can be 95% confident that his sample will include the population parameter.

(B) He can be 95% confused that his sample will include the population parameter.

(C) He can be 5% confident that his sample will not include the population parameter.

(D) He can be 5% confident that his sample will include the population parameter.

Choose the correct answer from the options given below:

Which of the following are correct about t-test statistics?

(A) The mean of t-test distribution is 0.

(B) It depends on the degrees of freedom.

(C) It depends on population standard deviation.

(D) With more degrees of freedom, it closely resembles standard normal distribution.

Choose the correct answer from the options given below:

A 95% confidence interval for a population mean was reported to be 152 to 160. If sample standard deviation $\sigma=15$, then sample size used in this study is (Given $Z_{0.025}=1.96$)

If n is the sample size of the population, then degree of freedom in t-distribution is

The following data are from a simple random sample: $6, 8, 11, 9, 15, 17$, then the point estimate of the population mean is

Consider the following hypothesis test:

$H_0: \mu \leq 16$

$H_a: \mu > 16$

A sample of 25 provided a sample mean $\bar{x} = 17$ and a sample standard deviation $s = 3.5$, then the value of the test statistic in $t$-test is:

Which one of the following statement is not correct?

Consider a random sample of 10 students having 116 cm as mean height and standard deviation as 9.798 cm. If the suggested mean height of the students population is 110 cm then the t-test statistic of the sample is:

[given $\frac{\sqrt{10}}{9.798} = 0.3227$]

If the following data is obtained from a simple random sample:

6, 7, 9, 10, 11, 17

Then the point estimate of population standard deviation is:

Which of the following statements are correct about the "Central Limit Theorem"?

(A) The sampling distribution of the sample mean approaches the normal distribution as the sample size gets larger.

(B) A sample size of 30 or more is considered to be sufficient to hold the "Central Limit Theorem".

(C) As the sample size becomes larger, the prediction of characteristics of the population becomes more accurate.

(D) The sampling distribution of the sample mean approaches a bell shaped curve as the sample size gets larger.

Choose the correct answer from the options given below:

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

Which of the following are correct?

(A) The probability curve in t-distribution is symmetric about the line t=0.

(B) t-axis is an asymptote of the curve.

(C) The variable t of t-distribution ranges from $-\infty$ to $\infty$

(D) As the number of degrees of freedom increases, the t-distribution curve moves closer to the binomial distribution.

Choose the correct answer from the options given below:

If we reject the null hypothesis when it is true, we might be making

If 95% confidence interval for the population mean was reported to be 140 to 150 and $\sigma = 25$, then size of the sample used in this study is:

[Given: $Z_{0.025} = 1.96$]