Question

A study on the latest fad diet claimed that the amounts of weight lost by all people on this diet had a mean of 22.8
pounds and a standard deviation of 6.2
pounds.
Step 2 of 2 : If a sampling distribution is created using samples of the amounts of weight lost by 69
people on this diet, what would be the standard deviation of the sampling distribution of sample means? Round to two decimal places, if necessary.
GPT 3.5
To find the standard deviation of the sampling distribution of the sample means, we use the formula:

Standard deviation of the sampling distribution = standard deviation / sqrt(sample size)

Given:
Standard deviation = 6.2 pounds
Sample size = 69 people

Standard deviation of the sampling distribution = 6.2 / sqrt(69)
Standard deviation of the sampling distribution = 6.2 / 8.3066
Standard deviation of the sampling distribution ≈ 0.746

Therefore, the standard deviation of the sampling distribution of sample means is approximately 0.75 pounds.

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