Question

f a sampling distribution is created using samples of the amounts of weight lost by 51 people on this diet, what would be the standard deviation of the sampling distribution of sample means

Answer 1

This question is incomplete, the complete question is;

A study on the latest fad diet claimed that the amounts of weight lost by all people on this diet had a mean of 24.6 pounds and a standard deviation of 8.0 pounds.

Step 2 of 2 : If a sampling distribution is created using samples of the amounts of weight lost by 51 people on this diet, what would be the standard deviation of the sampling distribution of sample means? Round to two decimal places, if necessary.

Answer:

the standard deviation of the sampling distribution of sample means is 1.12

Step-by-step explanation:

Given the data in the question,

population mean; μ = 24.6  pounds

Population standard deviation; σ = 8.0 pounds

sample size; n = 51

Now determine the standard deviation of the sampling distribution of sample means.

standard deviation of the sampling distribution of sample means is simply

⇒ population standard deviation / √sample size

= 8.0 / √51

= 8.0 / 7.141428

= 1.120224 ≈ 1.12

Therefore, the standard deviation of the sampling distribution of sample means is 1.12