Question

Lucy is using a one-sample t‑test based on a simple random sample of size n=27 to test the null hypothesis H0:μ=8.000 cm against the alternative H1:μ<8.000 cm. The sample has mean x⎯⎯=8.137 cm and standard deviation is s=0.822 cm. Determine the value of the t‑statistic for this test. Give your answer to three decimal places.

Answer 1

Answer: t= 0.866

Step-by-step explanation:

Formula to find t-test statistic :

$t=\dfrac{\overlien{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}$

where, n= sample size

$\overline{x}$= sample mean

$\mu$= Population mean

$s$=sample standard deviation

Given : Null hypothesis : H0:μ=8.000 cm

Alternative hypothesis : H1:μ<8.000 cm , since alternative hypothesis is one-tailed , so the test is one-tailed test.

$n= 27\\ \overline{x}=8.137\ cm\\ s=0.822\ cm$

Then , the t‑statistic for this test will be :-

$t=\dfrac{8.137-8.000}{\dfrac{0.822}{\sqrt{27}}}$

$t=\dfrac{0.137}{0.15819}=0.86604715848\approx0.866$

Hence, the value of the t‑statistic for this test : t= 0.866