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

Consider the following hypothesis test :

$H_0: \mu \le 35$

$H_a: \mu > 35$

A sample of 49 provided a sample mean of 38.2 The population standard deviation is 8. The value of test-statistic is,

A random sample consists of five observations: 2,4,5,6,8. The point estimate of the population mean is :

Match the LIST-I with LIST-II

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The following data are from a simple random sample: 8, 11, 13, 10, 13, 17. The point estimate of the population mean is:

If the average rainfall in a given area is 8 inches and the following table represents the average rainfall for four consecutive years, then the value of test statistic 't' is_____.

Match List-I with List-II

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In reference to the Inferential Statistics, which of the following statements are correct?

A. The number of degrees of freedom of a statistic is the number of independent varieties used to compute the statistic.

B. A confidence interval is a range that could be expected to contain the population parameter of interest.

C. In a hypothesis test, the significance level is the probability of making wrong decision when the null hypothesis is true.

D. The confidence level of the sampling distribution of a statistic is known as its standard error.

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Match the LIST-I with LIST-II

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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 standard deviation of 0.063 cm. If $t_9(0.05)=2.262$, then which of the following is NOT correct?

Which of the following are correct?

(A) The central limit theorem (CLT) states that the sampling distribution of the sample approaches a normal distribution as the sample size gets larger, no matter what is the shape of the population distribution.

(B) The measurable characteristic of population is called parameter.

(C) The population focuses on the identification of the characteristic.

(D) The sample makes inference about the population.

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Consider the following hypothesis test:

$H_o: \mu \le 12$

$H_a: \mu > 12$

A sample of 25 provided a sample mean $\bar x=14$ and a sample standard deviation $s=4.32$. The degree of freedom is

A simple random sample of 64 items from a population with standard deviation $\sigma=4$ resulted in a sample mean of 35. What is the margin of error for the population mean at a 95% confidence level? (Given $Z_{0.025}=1.96$)

The normal distribution is called as standard normal distribution when

If the sample size is 45, then the degree of freedom is equal to

Match the terms mentioned List I with the definitions mentioned in List II.

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For the following data from the simple random sample: 4, 7, 9, 8, 11, 15, the point estimate of the population mean will be

For the data from the simple random sample as: 5, 8, 10, 7, 18, 12

The point estimate of the population standard deviation is

A company produces an item M whose mean sales per shop per month was found to be 84 dozens. After an advertisement, a sample of 26 shops was taken and mean sales was found to be 80 dozens with standard deviation of 9. Based on this data, which of the following is true?

(Given $t_{25}(0.05) = 2.06$)

[t = t-test statistic]

The value of t-statistic for the following data as Population mean is 51, Sample mean is 54, Sample size is 10 and sample variance is 36, is:

A simple random sample of 49 items from a population with standard deviation 10 resulted in a sample mean of 25. Then the 95% confidence interval for population mean are :

(Given $z_{\alpha/2} = 1.96$ where $\alpha = 0.05$)

The sampling distribution of the sample mean approaches a normal distribution as the sample size gets larger, no matter what is the shape of the population distribution.

The above statement is:

A company has been producing steel tubes of mean inner diameter of 3 cm. A sample of 17 tubes gives an inner diameter of 3.01 cm and a standard deviation of 0.064. Then the value of the t-test statistic is:

A sample of 100 LED TVs is taken at random. Out of 100 we found 35 TVs are of Sony, 50 are of LG and 15 are of Samsung. The point estimate of population proportion of LG is

The monthly sales of a plywood shop are normally distributed with a standard deviation of ₹900. A statistical study of sales in the last nine months has found a confidence interval for the mean monthly sales with extremes ₹4663 and ₹5839. What were the average sales over the nine-month period?

In a confidence interval, the range of values above and below the sample statistic is called :

Which of the following are true ?

(A) If the mean of a normal variate is 12 and standard deviation is 4, then the Z-score of data point 20 is 2.

(B) Mean of the numbers obtained on throwing a die having '1' on three faces, '2' on two faces and '5' on one face is 3.

(C) If the variance of a Poisson's distribution is 2, then $P(X=0)=\frac{1}{e^2}$.

(D) For a binomial distribution, mean = 9 and the standard deviation is $\frac{3}{2}$, then the number of trials is 12.

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Consider the following hypothesis test

$H_0: \mu\le3530$

$H_a: \mu>3530$

A sample of 100 provided a sample mean of $\bar x=3740$ and population standard derivation $S=700$. What is the value of t-statistic ?

Which of the following is not a rejection rule for one sample t-test: (Where α is the level of significance)

(A) Reject null hypothesis $H_0$ : if $t \leq -t_\alpha$.

(B) Reject null hypothesis $H_0$ : if $t \geq -t_\alpha$.

(C) Reject null hypothesis $H_0$ : if $t \geq t_\alpha$.

(D) Reject null hypothesis $H_0$ : if $t \leq -t_{\alpha/2}$ or $t \geq t_{\alpha/2}$.

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As per the concept of inferential statistics, population stands for:-

A sample of size 9 from a normal population with sample mean $\bar{X} = 15.8$ and population estimated standard deviation $\sigma = 3.21$, then 99% confidence interval for population mean is : $(Use: t_8(0.01) = 3.335)$