A sample of 25 speedometers is selected to test whether they should be installed in automobiles.
a) In the USA, where the speed limit is 55 mph, what is the appropriate H0 / H1 pair, written in terms of the true mean speed [tex]\mu_{x}[/tex] ? Hint: you need to consider “good” / bad errors.
b) Data accompanying this study give [tex]\bar{x}[/tex] =53.87 ; [tex]Sx[/tex] = 2.70. Compute the p-value.
c) What is the conclusion at [tex]\alpha[/tex] =0.05 ?
Answer:
Check below for proper explanation
Step-by-step explanation:
a)
[tex]H_0:[/tex] [tex]\mu[/tex] [tex]\geq[/tex] 55
[tex]H_1:[/tex] [tex]\mu[/tex] < 55
b)
Test statistic:
z=[tex]\frac{(53.87-55)}{\frac{2.70}{\sqrt{25} } }[/tex]
z= [tex]-2.093[/tex]
Now; the p-value =[tex]P(z<-2.093)[/tex] = [tex]0.0182[/tex]
We can therefore conclude that; since the p-value < 0.05, we reject the null hypothesis, as such the speed as well is less than 55 mph.
