UI STAT 251 Spring 2011 Quiz 12 NAME: UI-ID:
1. The mean yield of corn in the United States is about 120 bushels per acre. A survey of 40 farms this year gives a sample mean yield of = 123.8 bushels per acre, and a sample standard deviation is 10.2 bushels per acre. We want to know whether this is good evidence that the national mean this year is not 120 bushels per acre. Assume that the sample of farms surveyed is a simple random sample from the population of all commercial corn growers. Carry out an appropriate hypothesis test for the situation by clearly writing down all steps involved.
1st
H0:μ=120
Ha:μ≠120
2nd
SEy=10.240=1.62
3rd
t=y-μ0SEy=123.8-1201.62=2.35
> 1-pt(2.35,39)
[1] 0.01196408
P value= 2*0.012=0.024
P value<0.05, we reject the null hypothesis, which means that the national mean this year is not 120 bushels per acre.
2. Poisoning by the pesticide DDT causes tremors and convulsions. In a study of DDT poisoning, researchers fed several rats a measured amount of DDT. They then measured electrical characteristics of the rats' nervous systems that might explain how DDT poisoning causes tremors. One important variable was the ‘absolutely refractory period,’ the time required for a nerve to recover after a stimulus. This period varies normally. Measurements on a random sample of rats gave the data below (in milliseconds).
1.6 1.7 1.8 1.9 1.7 1.8 1.6
Give a 90% confidence interval for the mean ‘absolutely refractory period’ for all rats of this strain when subjected to the same treatment.
> x=c(1.6,1.7,1.8,1.9,1.7,1.8,1.6)
> mean(x)
[1] 1.728571
> sd(x)
[1] 0.1112697
> qt(0.95,6)
[1] 1.943180
The confidence interval is:
y±t×SEy=1.73±1.94*0.117=(1.65,1.81)