Question

A sample of 260 one-year-old baby boys in the United States had a mean weight of 25.5 pounds. Assuming a population standard deviation of 4.1 pounds, what is the upper bound of the 90% confidence interval for the mean weight?

a) 27.15 pounds
b) 27.32 pounds
c) 26.45 pounds
d) 26.78 pounds

Answer 1

The upper bound of the 90% confidence interval for the mean weight of one-year-old baby boys in the United States is 27.32 pounds. Thus, the correct option is b. 27.32 pounds.

Step-by-step explanation:

To calculate the upper bound of the confidence interval, we use the formula:
`\[ \text{Upper Bound} = \text{Mean} + Z * \left( \frac{\text{Standard Deviation}}{\sqrt{\text{Sample Size}}} \right) \].` In this case, the mean weight is given as 25.5 pounds, the population standard deviation is 4.1 pounds, the sample size is 260, and the Z-value for a 90% confidence interval is approximately 1.645.

Substituting these values into the formula:
`\[ \text{Upper Bound} = 25.5 + 1.645 * \left( (4.1)/(√(260)) \right) \].` After performing the calculation, the upper bound is found to be approximately 27.32 pounds.

The Z-value is determined based on the desired confidence level, and in this case, for a 90% confidence interval, it corresponds to 1.645 standard deviations from the mean in a standard normal distribution. The formula considers the mean, standard deviation, and sample size to provide a range within which we can be 90% confident that the true population mean weight lies.

Therefore, the upper bound of 27.32 pounds signifies that, with 90% confidence, the mean weight of one-year-old baby boys in the United States is expected to be below this value. This statistical approach allows for a reasonable estimation of the true population parameter based on a sample. Thus, the correct option is b. 27.32 pounds.