Answer to Question #189066 in Statistics and Probability for Hania

Question

ten dry cells were taken from store and voltage tests gave the following results: 1.52,1.53,1.49,1,48,1.47,1.49,1.51,1.50,1.47,1.48 volts. the mean voltage of the cells when stored was 1.51v. assuming the population standard deviation to remain unchanged at 0.02v,

Answer 1

Given , mean say $x=1.51$

Let $H_o:\mu_o\ge1.51,$ The mean voltage of the cell greater than 1.51 volts.

and $H_a:\mu_o <1.51$ , The mean voltage of the cell is not greater than 1.51 volts.

Population mean, $\mu=\dfrac{14.94}{10}=1.494 ,\text{ Population standard deviation } \sigma=0.02$

Sample size, $n=10$

using t-test for independent sample

Test statistics-

$t=\dfrac{x-\mu}{\frac{\sigma}{\sqrt{n}}}=\dfrac{1.51-1.494}{\frac{0.02}{\sqrt{10}}}=0.9486$

The value of t at 5% level of significance and degree of freedom (n-1) i.e. 9 is 1.895.

Conclusion: As calculated value of t is less than the tabular value of 1.895. So Null hypothesis is accepted. The mean voltage of the cell greater than 1.51 volts.