CUET Mathematics: Statistics & ApplicationsInferential. Free, no login required.

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

(A) Point estimation

(B) Interval estimation

(C) Marginal estimation

(D) Hypothesis testing

Choose the correct answer from the options given below:

Consider the following hypothesis test:

$H_0: \mu = 18$

$H_1: \mu \neq 18$

If a sample of 48 provided a sample mean $\bar{x} = 17$ and a sample standard deviation $\sigma = 4.5$, then the value of the t-test statistic is:

The point estimate of the population standard deviation for the random sample 5, 8, 10, 7, 10, 14 is:

Which of the following are correct?

(A) A statistical hypothesis is a statement about the population parameter which may be true or false.

(B) In a statistical hypothesis testing procedure, a Type I error is made when the null hypothesis is accepted when it is false.

(C) In a statistical hypothesis testing procedure, a Type II error is made when the null hypothesis is rejected when it is true.

(D) The number of degrees of freedom of a statistic is the number of independent variates used to compute that statistic.

Choose the correct answer from the options given below:

A machine has been producing steel tubes of mean inner diameter of 2 cm. A sample of 10 tubes gives an inner diameter of 2.01 cm and a standard deviation of 0.063 cm. Test the hypothesis that the machine is working in the proper order at 5 % level of significance and answer, which of the following statements are correct?

[Given that : t₉(0.05) = 2.262]

(A) The value of the test statistic is t = 0.476.

(B) The null hypothesis is rejected at 5 % level of significance.

(C) The null hypothesis is accepted at 5 % level of significance.

(D) The degree of freedom is 10.

Choose the correct answer from the options given below:

Let two independent random samples of sizes $n_1$ and $n_2$ respectively have been drawn from the same normal population. Let $\overline{X_1}$ and $\overline{X_2}$ be the means and let $s_1$ and $s_2$ be their standard deviations. In order to test whether the the two sample means $\overline{X_1}$ and $\overline{X_2}$ differ significantly or not, the $t$-test statistic is given by

In reference to the Inferential Statistics, which of the following is NOT correct?

A company has been producing steel tubes of mean inner diameter of 2 cm. A sample of 10 tubes gives an inner diameter of 2.01 cm and a variance of 0.0004 cm². The value of test statistic is :

Which of the following is not correct about the Central Limit Theorem?

Let us suppose that two independent random samples of sizes $n_1$ and $n_2$ has been drawn from the same normal population then degree of freedom of statistic t-distribution is:

A 95 % confidence interval states that the population mean is greater than 152 and less than 160. If $\sigma = 15$ and $Z_{0.025} = 1.96$, then what sample size was used in the study?

A specific characteristic of a sample is known as a

The simple random sample consists of six observations: 5, 8, 10, 7, 10, 14. The point estimate of the population mean is:

Match List-I with List-II

Choose the correct answer from the options given below:

Which of the following are the assumptions underlying the use of t-distribution?

(A) The variance of population is known.

(B) The samples are drawn from a normally distributed population.

(C) Sample standard deviation is an unbiased estimate of the population variance.

(D) It depends on a parameter known as degree of freedom.

Choose the correct answer from the options given below:

If a 95% confidence interval for a population mean was reported to be 132 to 160 and sample standard deviation $\sigma = 50$, then the size of the sample in the study is:

(Given $z_{0.025} = 1.96$)

Arrange the following as per statistical inferences:

(A) Data Analysis

(B) Population

(C) Making Inferences

(D) Data Collection

Choose the correct answer from the options given below:

Which of the following is NOT correct about the Central Limit Theorem?

When the two independent small samples of sizes $n_1$ and $n_2$ with means $\bar{x}_1$ and $\bar{x}_2$ respectively are drawn from populations with identical population variances, the test-statistic is computed as

A measurable characteristic of a population is called _____.

Consider the following hypothesis test:

$H_0: \mu \leq 12$

$H_a: \mu > 12$

A sample of 25 provided a sample mean $\bar{x} = 14$ and a sample standard deviation $s = 4.32$. If $t_{0.05} = 1.711$, then which of the following is correct?

(A) The test statistic is defined as $t = \frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}}$.

(B) The value of the test statistic is 1.31.

(C) At $\alpha = 0.05$, the null hypothesis is rejected.

(D) If the value of the t-statistic is less than $t_\alpha$, then null hypothesis is accepted.

Choose the correct answer from the options given below:

The following data is from a simple random sample :

$15,23, x, 37,19,32$

If the point estimate of the population mean is $23$, then the value of $x$ is :

If $95 \%$ confidence interval for the population mean was reported to be $160$ to $170$ and $\sigma=25$, then size of the sample used in this study is: (Given $\mathrm{Z}_{0.025}=1.96$ )