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.

Accepted Solution

Answer: t= 0.866Step-by-step explanation:Formula to find t-test statistic : [tex]t=\dfrac{\overlien{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]where, n= sample size[tex]\overline{x}[/tex]= sample mean[tex]\mu[/tex]= Population mean[tex]s[/tex]=sample standard deviationGiven : 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. [tex]n= 27\\ \overline{x}=8.137\ cm\\ s=0.822\ cm[/tex]Then , the t‑statistic for this test will be :-[tex]t=\dfrac{8.137-8.000}{\dfrac{0.822}{\sqrt{27}}}[/tex][tex]t=\dfrac{0.137}{0.15819}=0.86604715848\approx0.866[/tex]Hence, the value of the t‑statistic for this test : t= 0.866