to different sampling distributions in the decreasing order of their standard error.
A. $\sigma=1.6$, $\eta=16$
B. $\sigma=1.5$, $\eta=25$
C. $\sigma=0.6$, n=36
D. $\sigma=1.4$, $\eta=49$
Choose the correct answer from the options given below :
Standard Error Calculation and Ordering
The standard error (SE) of a sampling distribution measures the variability of sample means. It is calculated using the formula:
$SE = \(\frac{\sigma}{\sqrt{n}}\)$
where $\(\sigma\)$ is the standard deviation and $\(n\)$ is the sample size.
To arrange the given options in decreasing order of their standard error, we calculate the SE for each pair:
Standard Error Calculations
| Option | Standard Deviation ($\(\sigma\)$) | Sample Size ($\(n\)$) | Standard Error (SE) Calculation | SE Value |
|---|---|---|---|---|
| A | 1.6 | 16 | $\(\frac{1.6}{\sqrt{16}} = \frac{1.6}{4}\)$ | 0.4 |
| B | 1.5 | 25 | $\(\frac{1.5}{\sqrt{25}} = \frac{1.5}{5}\)$ | 0.3 |
| C | 0.6 | 36 | $\(\frac{0.6}{\sqrt{36}} = \frac{0.6}{6}\)$ | 0.1 |
| D | 1.4 | 49 | $\(\frac{1.4}{\sqrt{49}} = \frac{1.4}{7}\)$ | 0.2 |
Ordering Based on Standard Error
Now, we arrange the calculated SE values in decreasing order:
- SEA = 0.4
- SEB = 0.3
- SED = 0.2
- SEC = 0.1
The decreasing order is A, B, D, C.
Correct Option Selection
This order corresponds to Option 2 in the given choices. However, the provided correct answer is Option B, which lists the order as A, B, D, C. This matches our calculated order.
Therefore, the correct arrangement is A, B, D, C.
Important Questions from Sampling
The process of converting the analog sample into discrete form is called ______.
Respondents of a recent sample survey provided names of friends they thought would be likely users of a new product. These friends were contacted, completed a survey, and asked to supply names of other likely users. Which method of sampling has been used in this survey ?
Which one among the following relates to the probability-based sampling technique?
In which process is the flat-top pulse amplitude modulated signal generated?
Consider a population of 3 units having values 2, 4 and 6. A simple random sample (without replacement) of 2 units is to be drawn from the population. Let M denote the sample mean of this sample. Then which of the following statements are true?
