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Lucy is using a one-sample t ‑test based on a simple random sample of size n = 22 to test the null hypothesis H 0 : μ = 16.000 cm against the alternative H 1 : μ < 16.000 cm. The sample has mean ¯¯¯ x = 16.218 cm and standard deviation is s = 0.764 cm. Determine the value of the t ‑statistic for this test. Give your answer to three decimal places.

Respuesta :

Answer:

The value of test statistic is 1.338

Step-by-step explanation:

We are given the following in the question:  

Population mean, μ = 16.000

Sample mean, [tex]\bar{x}[/tex] = 16.218

Sample size, n = 22

Alpha, α = 0.05

Sample standard deviation, s = 0.764

First, we design the null and the alternate hypothesis

[tex]H_{0}: \mu = 16.000\text{ cm}\\H_A: \mu < 16.000\text{ cm}[/tex]

We use one-tailed t test to perform this hypothesis.

Formula:

[tex]t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }[/tex]

Putting all the values, we have

[tex]t_{stat} = \displaystyle\frac{16.218 - 16.000}{\frac{0.764}{\sqrt{22}} } = 1.338[/tex]

Thus, the value of test statistic is 1.338

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