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 th

Question

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.

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Adalyn 3 months 2021-10-26T11:16:06+00:00 1 Answer 0 views 0

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    2021-10-26T11:17:39+00:00

    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, \bar{x} = 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

    H_{0}: \mu = 16.000\text{ cm}\\H_A: \mu < 16.000\text{ cm}

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

    Formula:

    t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }

    Putting all the values, we have

    t_{stat} = \displaystyle\frac{16.218 - 16.000}{\frac{0.764}{\sqrt{22}} } = 1.338

    Thus, the value of test statistic is 1.338

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