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

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A 95% confidence interval for a population mean was reported to be 152 to 160. The margin of error is:

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If X is normally distributed with mean 30 and standard deviation 5, the value of $P(26 \le X \le 34)$ is: (Where $P(0 \le Z \le 0.8) = 0.2881$)

Tamanna was researching on problem of under-age workers at factories. She met a suitable child and interviewed him. He put her in contact with three another workers. Those three workers brought her in contact with ten other underage workers. This process of sampling is known as:

A random sample of 17 values from a normal population has a mean of 105 cm and the sample standard deviation is 8.489. If normal population mean is 110 cm, then the upper limit of confidence at 5% level of significance is : (Given $t_{16}(0.05) = 2.12$)

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In a survey question for a sample of 340 people, 85 persons gave positive response, 145 people gave negative response and 110 people were neutral, gave no response. What is the point estimate of the proportion in the population who respond positive?

Which of the following points describe the concept of population in inferential statistics ?

A. It is a collection of all elements having same characteristics.

B. A survey done on the total population is not accurate.

C. Population focuses on the identification of the characteristic.

D. Population focuses on drawing inference about the sample.

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The monthly salaries of workers in a garment factory are normally distributed. The mean salary is ₹ 10,000 and standard deviation is ₹ 625. If 2,500 workers are getting salary less than ₹ 10,000, then the total number of workers in the factory is:

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

Consider the following hypothesis test:

$H_0: \mu \leq 25$

$H_a: \mu > 25$

A sample of 25 provided a sample mean of 27.80. The population standard deviation is 5, then the value of the test statistic is

Which of the following statements are correct?

(A) A sample size of 30 or more is considered to be sufficient to hold the central limit theorem.

(B) A survey done using a sample of the population has no margin of error.

(C) The measurable characteristic of a population is called parameter.

(D) The sample makes an inference about the population.

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Which of the following statements are correct?

A. The measurable characteristic of a population is called parameter.

B. Sample is a subgroup of members of the population.

C. Population is a collection of all elements having the same characteristics.

D. The difference between a population parameter and a sample statistic is known as sampling error.

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The central limit theorem states that the sampling distribution of the sample mean approaches the 'X' distribution, as the sample size gets larger, no matter what the shape of the population is, then 'X' is

A simple random sample of 49 items from a population with standard deviation, σ = 6 resulted in a sample mean of 32. At 95% confidence level, the margin of error is (Given $Z_{0.025} = 1.96$)

If the sample size ($n$) is 32 in testing of hypothesis by t-test, then the degree of freedom ($\gamma$) is equal to :

The following data are from a simple random sample: 3, 6, 8, 15, 5, 11. What is the point estimate of the population mean?

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Which of the following statements are TRUE?

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

(B) The probability curve of the t-distribution is symmetric about the line $t=0$

(C) The variance of the t-distribution is greater than one.

(D) As the number of degrees of freedom decreases, the t-distribution curve moves closer to the standard normal probability curve.

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For the following data:

The sample statistic t follows t-distribution with 'm' degrees of freedom, then m is equal to

The following data are from a random sample: 5,8,10,7,10,14, then the point estimate of the population standard deviation is

A small start-up started making wafers and distributing them to the retailers. After a week, average sales per week were found to be 150 packets. So, to increase the sales, a strategy was used to change the packaging and add a chocolate worth Rs. 5 as a free gift with the pack. After this, a sample of 17 shops was taken, which showed that sales went up with mean 165 and a standard deviation of 25. Check whether the strategy was effective @5%, level of significance ? [Given $t_{16} (0.05) =2.12$]

The marks obtained by five students in a test of Applied Mathematics carrying 100 marks are 49, 58, 67, 92, 99. Then the point estimate of the population mean is

Consider the following hypothesis

$H_0: \mu = 315$ and $H_a: \mu \neq 315$

A sample of 60 provided a sample mean of 324.6. The standard deviation ($\sigma$) is 14 and level of significance $\alpha = 0.05$. Then the confidence interval is:

[Given: $Z_{a/2}{\frac{14}{\sqrt60}} = 3.54$]

If $x_1, x_2, x_3, ..., x_n$ are n observations in a sample then which of following is/are TRUE?

(A) The mean $\bar{x}$ has n degree of freedom

(B) The mean $\bar{x}$ has (n-1) degree of freedom

(C) The standard deviation of the sample has (n-1) degree of freedom

(D) The standard deviation of the sample has n degree of freedom

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For 95% confidence interval for a population mean reported to be 132 to 142 with standard deviation $\sigma = 17.85$ then the sample size used in this case, is:

[Given that: $Z_{0.125} = 1.96$]

A random sample of size 16 has 53 as mean. The sum of the squares of the deviations taken from mean is 150. If the population mean is 56 then the value of t-test statistic is:

If a 99% confidence interval states that the population mean is greater than 100 and less than 400. Then the sample mean and margin of error respectively are: