CUET Mathematics Applied Mathematics > Inferential Statistics PYQs

Match the LIST-I with LIST-II | LIST-I | | LIST-II | |---|---|---| | A. | The measurable characteristic of a population is called | I. Statistic | | B. | The measurable characteristic of a sample is called | II. Confidence level | | C. | The percentage of all possible samples that can be expected to include the true population parameter is called | III. Confidence interval | | D. | A range that could be expected to contain the population parameter of interest is | IV. Parameter | Choose the correct answer from the options given below:

A simple random sample consists of five observations: 2, 4, 6, 7,11, then which of the following are true ? A. Sample mean = 7.5 B. Sample mean = 6 C. Sample standard deviation = $\sqrt{11}$ D. Sample standard deviation = $\sqrt{11.5}$ Choose the correct answer from the options given below:

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

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

Match the LIST-I with LIST-II | LIST-I (Term) | | LIST-II (Definition) | |---|---|---| | A. Confidence level | | I. In a confidence interval, the range of values, above and below the sample statistic. | | B. Margin of error | | II. It is the probability of making Type-I error, when null hypothesis is true as an equality. | | C. Level of significance | | III. It involves the use of sample data to calculate a single value of an unknown population parameter. | | D. Point estimation | | IV. It describes the uncertainty of a sampling method. | Choose the correct answer from the options given below:

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:

In a hypothesis test, the probability of making the wrong decision when the null hypothesis is true is called

Given that the mean of the normal variate X is 10 and the standard deviation is 2, then what will be the z-score of the data point 16 ?

Five students are selected at random from a school and their weights are found to be 50, 51, 53, 54 and 62. The point estimation of the population mean is:

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:

A Simple random sample consists of four observation 1, 3, 5, 7. The point estimate of population standard deviation is

Which of the following is a statistic ?

Which of the following is false about the central limit theorem

Out of 1000 employees, 100 have to be selected for a survey . After being arranged in the alphabetical order each one is assigned a number from 1 to 1000. A number 4 is selected and then every 10th person is selected (i.e 4 , 14, 24 ... ) . Which form of sampling is this an example of ?

Which of the following is not a statistic ?

T- test : A t- test is a test of difference for parameter data $t = \frac{\overline{x1} - \overline{x2}}{s\sqrt{\frac{1}{n1} + \frac{1}{n2}}}$ Then read the following statements and choose the correct statements (A) the null hypothesis and the alternative hypothesis have the same viewpoint (B) In t- test testing the significance of mean value is done, when sample size is small (C) T - test for two independent groups when variance is equal (D) Testing is a process used by statisticians to accept or reject the hypothesis (E) if the value of test statistics is greater than the table values, we do not reject the null hypothesis Choose the correct answer from the options given below :

Consider the following hypothesis test : $H_0 : \mu \leq 24$, $H_a : \mu > 24$ A sample of 64 provided a sample mean of 24.3 . The population standard deviation is 2. The value of the test statistic is :

The following data is available for two independent sample: | | SAMPLE-1 | SAMPLE-2 | |---|---|---| | sample size | 8 | 10 | | sample mean | 191 | 199 | | sample standard deviation | 10 | 12 | Then the value of t-statistic is :

In the formula for Z-test statistic $Z = \frac{\bar{x} - \mu_0}{\frac{\sigma}{\sqrt{n}}}$, mark the incorrect statement.

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

The assumption opposite of what is made in the null hypothesis is known as the _________ hypothesis.

Match **List - I** with **List - II**. | | List - I | | List - II | |---|---|---|---| | (A) | Left tailed test | (I) | $H_0 : \mu = 50$ | | (B) | Two tailed test | (II) | $H_1 : \mu > 50$ | | (C) | Null hypothesis | (III) | $H_1 : \mu < 50$ | | (D) | Right tailed test | (IV) | $H_1 : \mu \neq 50$ | Choose the **correct** answer from the options given below :

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 :

A simple random sample consists of five observations 2, 4, 7, 12, 15. The point estimate of the population mean is :

The standard deviation of a sampling distribution of a statistic is also known as :

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 :

Consider the following hypothesis test : $H_0 : \mu \leq 20$ $H_1 : \mu > 20$ A sample of 81 produced a sample mean of 20.55. The population standard deviation is 3. The value of the test statistic is :

A simple random sample consists of four observations 7, 8, 10, 7. The point estimate of population standard deviation is :

Match List - I with List - II. | List - I | List - II | |----------|-----------| | (A) A special characteristic of a population is called | (I) Sample Size | | (B) The number of statistical individuals in a sample is called | (II) Statistic | | (C) A special characteristic of a sample is called | (III) Standard error | | (D) The standard deviation of the sampling distribution of a statistic is known as its | (IV) Parameter | Choose the correct answer from the options given below :

Which of the following statements are true ? (A) Central limit theorem states that the sampling distribution of the mean $(\bar{x})$ approaches a normal distribution as the sample size increases. (B) As per Central Limit Theorem, when the sample size increases, the mean $(\bar{x})$ for the data becomes closer to the mean of overall population. (C) The shape of t-distribution does not depend on degree of freedom. Choose the correct answer from the options given below :

Match List I with List II | LIST I | LIST II | |---|---| | A. A special characteristic of a population is known as a: | I. statistic | | B. A special characteristic of a sample is known as a: | II. Confidence interval | | C. The uncertainty of a sampling process is expressed by: | III. Estimation | | D. The process by which one makes the inferences about a population based on the information obtained from a sample is known as: | IV. Parameter | Choose the correct answer from the options given below:

From a population having a mean of 20 and standard deviation 2, a random sample of size 64 is taken and its mean is found to be 19.5. The test statistic to test that the sample is taken from the population is

From a sample of 5 items having values 2, 4, 6, 7, 6, the unbiased estimates of the population mean and the standard deviation are: