Questions: A hypothesis regarding the weight of newborn infants at a community hospital is that the mean is 10.1 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.1, 12.1, 13.1, 14.1, 10.1, 15.1, and 16.1 pounds. If α=0.010, what is the critical value? The population standard deviation is unknown. Multiple Choice 0 ± 3.203 ± 3.707

Solution Steps

To determine the critical value for a hypothesis test when the population standard deviation is unknown, we use the t-distribution. The steps are as follows:

1. Identify the sample size (n), which is 7 in this case.
2. Determine the degrees of freedom (df), which is \( n - 1 \).
3. Use the significance level (\(\alpha\)) to find the critical value from the t-distribution table or using a statistical function.

Given the sample size \( n = 7 \), the degrees of freedom (df) is calculated as: \[ \text{df} = n - 1 = 7 - 1 = 6 \]

The significance level is given as \( \alpha = 0.010 \).

Using the t-distribution table or a statistical function, we find the critical value for a two-tailed test with \( \alpha = 0.010 \) and \( \text{df} = 6 \). The critical value is: \[ t_{\alpha/2, \text{df}} = 3.707 \]

Final Answer