An extensive study in Antarctica concluded that the mean height of adult emperor

Question

An extensive study in Antarctica concluded that the mean height of adult emperor penguins in the wild is 45.5 in. Cassandra believes that captive emperor penguins have a greater mean height due to better nutrition. To test this idea, she decides to conduct a one-sample t-test to see if the mean height of captive emperor penguins is greater than 45.5 in. She selects a simple random sample of 28 penguins from different zoos around the country and has each penguin measured. The summary statistics of the sample are given below. Sample size n-28 Sample mean x 46.7 in Sample standard deviation s = 4.6 in The heights of emperor penguins are normally distributed, and there are no outliers in the sample. Construct the null and alternative hypothesis for the appropriate one-sample t-test for the mean height of captive emperor penguins Ho: Hi: 4.6 28 46.7 45.5 46.7 45.5 4.6 28

Explanation / Answer

Hypotheswis:
H0 : mu = 45.5
Ha : mu > 45.5

Hypothesis:
H0 : mu = 10.1
Ha : mu < 10.1

a)
Critical value = 6.314

b)
Critical value = 2.093

c)
Critical value = 2.581

a)
df = n -1 =3 -1 =2

b)

c)
The value t = 2.10is not significant at the 10%,5% or 1% levels

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