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

Explanation:

Formula to find t-test statistic :

`t=\frac{\overlien{x}-\mu}{(\sigma)/(√(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=(8.137-8.000)/((0.822)/(√(27)))`

`t=(0.137)/(0.15819)=0.86604715848\approx0.866`

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