a health care professional wishes to estimate the birth weight of infants how large a sample must she select to be 90% confident that the true mean is within 6 ounces of e sample mean. the standard deviation of birth weights is
is known to be 8 ounces
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birth weight of infants. a health care professional wishes to estimate the birth weights of infants. how large a sample must be obtained if she desires to be 90% confident that the true mean is within 2 ounces of the sample mean? assume sigma=8 ounces
To determine the sample size required, we can use the formula:
n = (Z * σ / E)^2
where:
n = sample size
Z = Z-score for the desired confidence level (in this case, for 90% confidence, Z = 1.645)
σ = standard deviation of the population (known to be 8 ounces)
E = maximum margin of error (in this case, 6 ounces)
Substituting the given values into the formula, we have:
n = (1.645 * 8 / 6)^2
n = (10.36 / 6)^2
n = 1.726 ^2
n ≈ 2.98
Since you cannot have a fraction of a sample, you will need to round up to the nearest whole number. Therefore, the healthcare professional should select a sample size of 3 to be 90% confident that the true mean is within 6 ounces of the sample mean.
To determine the sample size needed, we can use the formula for sample size calculation with a known population standard deviation:
n = (Z * σ / E)^2
Where:
n = sample size
Z = Z-value for the desired level of confidence (90% in this case)
σ = population standard deviation (8 ounces in this case)
E = margin of error (6 ounces in this case)
First, we need to find the Z-value corresponding to a 90% confidence level. This value can be obtained from a standard normal distribution table or using statistical software. For a 90% confidence level, the Z-value is approximately 1.645.
Substituting the given values into the sample size formula:
n = (1.645 * 8 / 6)^2
n = (10.36 / 6)^2
n = (1.726)^2
n ≈ 2.976
The sample size needed should be rounded up to the nearest whole number, so the healthcare professional should select a sample size of at least 3 infants to be 90% confident that the true mean birth weight is within 6 ounces of the sample mean.