# Standard deviation of sample mean

• ychych00
Additionally, the population standard deviation is known and the sample size is large enough to account for any potential skewness in the data.
ychych00
Suppose we have a large population of houses in a community. The average annual heating expense for each house is $400 with a population standard deviation of$25. A random sample of 25 houses had a sample mean of $380 and a sample standard deviation of$35.

1.What is the mean of the sampling distribution of the sample mean for samples of size 25 chosen from the population of all houses?

2.What is the standard deviation of the sampling distribution of the sample mean for samples of size 25 chosen from the population of all houses?

3. Is it safe to assume that the sampling distribution of the sample mean for samples of size 25 is normally distributed? Why or why not?

1. The mean of the sampling distribution of the sample mean for samples of size 25 chosen from the population of all houses is $400.2. The standard deviation of the sampling distribution of the sample mean for samples of size 25 chosen from the population of all houses is$25/√25 = \$5.3. Yes, it is safe to assume that the sampling distribution of the sample mean for samples of size 25 is normally distributed. This is because according to the Central Limit Theorem, the sampling distribution of the sample mean will be approximately normally distributed as long as the sample size is sufficiently large (in this case, 25 is considered sufficiently large).

## 1. What is the standard deviation of sample mean?

The standard deviation of sample mean is a measure of how much the sample means vary from the overall population mean. It is calculated by taking the square root of the variance.

## 2. How is the standard deviation of sample mean calculated?

The standard deviation of sample mean is calculated by taking the square root of the variance of the sample means. The sample means are the averages of multiple samples taken from the same population.

## 3. What does a higher standard deviation of sample mean indicate?

A higher standard deviation of sample mean indicates that the sample means are more spread out from the overall population mean. This means that the samples are more diverse and less representative of the population.

## 4. What is the significance of the standard deviation of sample mean in statistical analysis?

The standard deviation of sample mean is an important measure in statistical analysis as it helps in understanding the variability of the data and the accuracy of the sample means in representing the population mean. It is also used in calculating confidence intervals and testing hypotheses.

## 5. How does sample size affect the standard deviation of sample mean?

As the sample size increases, the standard deviation of sample mean decreases. This is because larger sample sizes provide a more accurate representation of the population mean and therefore the sample means are less spread out. This is known as the central limit theorem.

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