A hypothesis regarding the weight of newborn infants at a community hospital is that the mean is 6.6 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds. If $\alpha$ = 0.05, what is the critical t value?
A) -2.365
B) $\pm$1.96
C) $\pm$2.365
D) $\pm$2.447
E) -2.447

Question

A hypothesis regarding the weight of newborn infants at a community hospital is that the mean is 6.6 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds. If $\alpha$ = 0.05, what is the critical t value?
A) -2.365
B)  $\pm$1.96
C)  $\pm$2.365
D)  $\pm$2.447
E) -2.447

Quizplus · Accepted Answer

To find the critical t value, we need to use a t-distribution with n-1 degrees of freedom (where n is the sample size). In this case, n = 7, so the degrees of freedom is 7-1 = 6.

We are given the significance level (alpha) as 0.05, which means that the probability of rejecting the null hypothesis (that the mean weight is 6.6 pounds) when it is actually true is 5%.

Using a t-distribution table or calculator with 6 degrees of freedom and a significance level of 0.05, we can find the critical t value to be approximately 2.447 (rounded to three decimal places).

Therefore, the best choice is D) F1F1F1S1F1F1F102.447 as the critical t value.

A Hypothesis Regarding the Weight of Newborn Infants at a Community