Statistics & Applications

Inferential

Medium

applied

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

2.1

4.1

5.6

3.1

✅ Correct Option: 4

The data from the random sample is: 5, 8, 10, 7, 10, 14

The sample size is $n = 6$

The sample mean is:

$\bar{x} = \frac{5 + 8 + 10 + 7 + 10 + 14}{6}$

$\bar{x} = \frac{54}{6}$

$\bar{x} = 9$

Calculate the squared deviations from the mean:

$(5 - 9)^2 = (-4)^2 = 16$

$(8 - 9)^2 = (-1)^2 = 1$

$(10 - 9)^2 = (1)^2 = 1$

$(7 - 9)^2 = (-2)^2 = 4$

$(10 - 9)^2 = (1)^2 = 1$

$(14 - 9)^2 = (5)^2 = 25$

The sum of squared deviations:

$\sum(x_i - \bar{x})^2 = 16 + 1 + 1 + 4 + 1 + 25$

$\sum(x_i - \bar{x})^2 = 48$

The point estimate of the population standard deviation uses the sample standard deviation with $(n-1)$ in the denominator:

$s = \sqrt{\frac{\sum(x_i - \bar{x})^2}{n-1}}$

$s = \sqrt{\frac{48}{6-1}}$

$s = \sqrt{\frac{48}{5}}$

$s = \sqrt{9.6}$

$s = 3.1$

Therefore, the point estimate of the population standard deviation is $3.1$

2025: 3 June Shift 1

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

2026: 12 May Shift 2

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

2026: 12 May Shift 2

Match List-I with List-II

List-I (Types of Probability Sampling)	List-II (Characteristic)
(A) Simple random sampling	(I) Every member of the population is arranged in a particular order. The first member is selected at random and then the remaining members are selected at regular intervals.
(B) Systematic sampling	(II) The population is divided into subgroups and each subgroup has similar characteristics of the whole population.
(C) Stratified sampling	(III) Every member of the population has an equal chance of being selected.
(D) Cluster Sampling	(IV) The population is divided into subgroups based on the relevant characteristics

Choose the correct answer from the options given below:

2026: 18 May Shift 2

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?

2025: 21 May Shift 2

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

2025: 29 May Shift 2

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)

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

Solution

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