Question

The valve was tested on 270 engines and the mean pressure was 6.6 lbs/square inch. Assume the variance is known to be 0.49. If the valve was designed to produce a mean pressure of 6.5 lbs/square inch, is there sufficient evidence at the 0.1 level that the valve does not perform to the specifications

Answer 1

Answer:

$z=\frac{6.6-6.5}{\frac{0.7}{\sqrt{270}}}=2.347$      

The p value for this case would be given by"

$p_v =2*P(z>2.347)=0.0189$  

For this case since the p value is higher than the significance level we don't have enough evidence to conclude that the true mean is significantly different from 6.5 lbs/square inch at 10% of significance. So then there is not enough evidence to conclude that the valve does not perform to the specifications

Step-by-step explanation:

Information given

$\bar X=6.6$ represent the sample mean

$s=\sqrt{0.49}= 0.7$ represent the population deviation

$n=270$ sample size      

$\mu_o =6.5$ represent the value that we want to test    

$\alpha=0.1$ represent the significance level

z would represent the statistic

$p_v$ represent the p value for the test

Hypothesis to verify

We want to verify if the true mean for this case is equal to 6.5 lbs/square inch or not , the system of hypothesis would be:      

Null hypothesis:$\mu= 6.5$      

Alternative hypothesis:$\mu \neq 6.5$      

The statistic for this case is given by:

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

And replacing we got:

$z=\frac{6.6-6.5}{\frac{0.7}{\sqrt{270}}}=2.347$      

The p value for this case would be given by"

$p_v =2*P(z>2.347)=0.0189$  

For this case since the p value is higher than the significance level we don't have enough evidence to conclude that the true mean is significantly different from 6.5 lbs/square inch at 10% of significance. So then there is not enough evidence to conclude that the valve does not perform to the specifications