Question

The hypothesis H0: \mu=350H 0 : μ = 350 versus H_a:\mu<350H a : μ < 350 are examined using a sample of size n = 20. The one-sample t statistic has the value t=-1.68t = − 1.68. What do we know about the P-value of this test

Answer 1

Answer:

The statistic for this case is given $t =-1.68$

The degrees of freedom are given by:

$df =n-1= 20-1=19$

Since is a one-side lower test the p value would given by:  

$p_v =P(t_{19}$  

Step-by-step explanation:

Data given and notation  

$\bar X$ represent the sample mean  

$s$ represent the sample standard deviation  

$n=20$ sample size  

$\mu_o =350$ represent the value that we want to test  

$\alpha$ represent the significance level for the hypothesis test.  

z would represent the statistic (variable of interest)  

$p_v$ represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the mean is lower than 350, the system of hypothesis are :  

Null hypothesis:$\mu \geq 350$  

Alternative hypothesis:$\mu < 350$  

Since we don't know the population deviation, is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)  

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic  

The statistic for this case is given $t =-1.68$

P-value  

The degrees of freedom are given by:

$df =n-1= 20-1=19$

Since is a one-side lower test the p value would given by:  

$p_v =P(t_{19}$