Question

# In a test of H0: LaTeX: \mu μ = 10.8 against LaTeX: H_A H A :...

In a test of H0: LaTeX: \mu μ = 10.8 against LaTeX: H_A H A : LaTeX: \mu μ < 10.8, the sample data with sample size 20 from a normal distribution yielded a test statistic Tobs = -2.09. Bracket the p-value for the test.

A) 0.01 < p-value < 0.025

B) 0.05 < p-value < 0.10

C) 0.01 < p-value < 0.005

D) 0.025 < p-value < 0.05

We have given :

n = sample size = 20

μ = population mean = 10.8

To test : Ho : μ = 10.8 VS H1 : μ < 10.8

( it is left tailed test : one tailed test )

Test statistics : t = -2.09

df = degree of freedom = ( n -1 ) = 19

p value = P [ t < -2.03 ] ( use statistical table )

p value = 0.02515

D) 0.025 < p-value < 0.05

## Decision : we reject Ho if p value is less than alpha value using p value approach here p value is less than alpha value ( assume alpha = 0.05 ) we reject Ho .

## Conclusion : There is sufficient evidence to conclude that population mean is less than 10.8 .

at 5 % level of significance .