A hypothesis regarding the weight of newborn infants at a community hospital is that the mean is 22.1 pounds. a sample of seven infants is randomly selected and their weights at birth are recorded as 21.1, 25.1, 26.1, 27.1, 24.1, 31.1, and 31.1 pounds. if α = 0.010, what is the critical value? the population standard deviation is unknown.

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MrRoyal MrRoyal · Answer 1 · 2022-06-15T08:07:58+02:00

The critical value at the 0.010 significance level with 6 degrees of freedom are ±3.7074

The dataset is given as:

21.1, 25.1, 26.1, 27.1, 24.1, 31.1, and 31.1

The sample mean is:

[tex]\bar x = 22.1[/tex]

The significance level is

α = 0.010

Start by calculating the degrees of freedom using:

df = n - 1

Where n represents the sample size (n = 7)

So, we have:

df = 7 - 1

df = 6

Using the table for t critical values for a two-tailed test, we have:

Critical value = ±3.7074

Hence, the critical value at the 0.010 significance level with 6 degrees of freedom are ±3.7074