Question

Either use technology to find the P-value or use

Answer 1

Answer:

The first step is calculate the degrees of freedom, on this case:  

$df=n-1=21-1=20$  

Since is a one side left tailed test the p value would be:  

$p_v =P(t_{(20)}$  

And we can use the following excel code to find it: "=T.DIST(-0.024,20,TRUE)"

Step-by-step explanation:

Data given and notation  

$\bar X$ represent the mean

$s$ represent the sample standard deviation

$n=21$ sample size  

$\mu_o =140$ represent the value that we want to test

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

t=-0.024 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 for the widths of tornadoes is lower than 140 yd, the system of hypothesis would be:  

Null hypothesis:$\mu \geq 140$  

Alternative hypothesis:$\mu < 140$  

If we analyze the size for the sample is < 30 and we don't know the population deviation so 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 is given by: $t = -0.024$

P-value

The first step is calculate the degrees of freedom, on this case:  

$df=n-1=21-1=20$  

Since is a one side left tailed test the p value would be:  

$p_v =P(t_{(20)}$  

And we can use the following excel code to find it: "=T.DIST(-0.024,20,TRUE)"

Based on the p value obtained we can conclude that we FAIL to reject the null hypothesis at any significance level selected $\alpah=0.01,0.05,0.1$