Question

In performing a hypothesis test where the null hypothesis is that the population mean is 4.8 against the alternative hypothesis that the population mean is not equal to 4.8, a random sample of 25 items is selected. The sample mean is 4.1 and the sample standard deviation is 1.4. It can be assumed that the population is normally distributed. The observed t value for this problem is______.

Answer 1

Answer: -2.5

Step-by-step explanation:

Formula to calculate the t-test statistic (or t-value) for a test is given by :-

$t=\dfrac{\overline{x}-\mu}{\dfrac{s}{\sqrt{n}}}$

where , n= sample size

$\overline{x}$ = sample mean

$\mu$ = Population mean

s= sample standard deviation.

As per given we have,

$\mu= 4.8$

$\overline{x}=4.1$

s= 1.4

n= 25

Then, t-value will be

$t=\dfrac{4.1-4.8}{\dfrac{1.4}{\sqrt{25}}}$    (Substitute the values )

$\Rightarrow\ t=\dfrac{-0.7}{\dfrac{1.4}{5}}$  

$\Rightarrow\ t=\dfrac{-0.7}{0.28}$  

$\Rightarrow\ t=\dfrac{-70}{28}=\dfrac{-5}{2}=-2.5$  

Hence, the observed t value for this problem is t= -2.5