Statistics & Applications

Inferential

Medium

applied

A 95% confidence interval for a population mean was reported to be 152 to 160. If sample standard deviation $\sigma=15$ , then sample size used in this study is (Given $Z_{0.025}=1.96$ )

✅ Correct Option: 4

Given information:

Confidence interval: 152 to 160
$\sigma = 15$
$Z_{0.025} = 1.96$ (Z-value for 95% confidence)
Find: Sample size $(n)$

The sample mean is at the center of the confidence interval.

Sample mean $(\bar{x}) = \dfrac{152 + 160}{2}$

$\bar{x} = \dfrac{312}{2}$

$\bar{x} = 156$

The margin of error is the distance from the mean to either endpoint of the interval.

Margin of Error $(E) = 160 - 156$

$E = 4$

The margin of error formula for a confidence interval is:

$E = Z \times \dfrac{\sigma}{\sqrt{n}}$

Substituting the known values:

$4 = 1.96 \times \dfrac{15}{\sqrt{n}}$

$4 = \dfrac{29.4}{\sqrt{n}}$

$4\sqrt{n} = 29.4$

$\sqrt{n} = \dfrac{29.4}{4}$

$\sqrt{n} = 7.35$

$n = (7.35)^2$

$n = 54.0225$

$n \approx 54$

Therefore, the sample size used in this study is 54.

2025: 21 May Shift 2

Which of the following statements are correct about the "Central Limit Theorem"?

(A) The sampling distribution of the sample mean approaches the normal distribution as the sample size gets larger.

(B) A sample size of 30 or more is considered to be sufficient to hold the "Central Limit Theorem".

(D) The sampling distribution of the sample mean approaches a bell shaped curve as the sample size gets larger.

Choose the correct answer from the options given below:

2026: 18 May Shift 2

Match the LIST-I with LIST-II

LIST-I	LIST-II
A. Confidence interval	I. Sampling distribution of the sample mean approaches normal distribution as the sample size gets larger, no matter what the shape of the population distribution is.
B. Hypothesis	II. A measurable characteristic of a sample.
C. Central limit theorem	III. The amount of uncertainity associated with a sample estimate of a population parameter.
D. Statistic	IV. An educated guess which needs to be tested.

Choose the correct answer from the options given below:

2026: 30 May Shift 2

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

2025: 26 May Shift 2

Consider the following test:

H₀: μ ≤ 12

H₁: μ > 12

A sample of 36 provided a sample mean $\bar{x} = 16$ and a sample standard deviation S=4.2. Then the value of the t- test statistic is:

2025: 21 May Shift 1

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

2025: 30 May Shift 2

A random sample of 100 individuals provides 25 positive responses.

Then the point estimate of the population proportion with "positive" responses is:

A 95% confidence interval for a population mean was reported to be 152 to 160. If sample standard deviation σ=15\sigma=15σ=15, then sample size used in this study is (Given Z0.025=1.96Z_{0.025}=1.96Z0.025​=1.96)

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A 95% confidence interval for a population mean was reported to be 152 to 160. If sample standard deviation $\sigma=15$ , then sample size used in this study is (Given $Z_{0.025}=1.96$ )