Homework Week 3 Hypothesis testing
Question 1. Test the hypothesis
H0: μ=500
H1: μ≠500
Using the evidence �̅� = 530, s=90 from a sample of n=100, at a significance level of 1%.
Question 2. You buy cars for a car rental company, and want to buy 20 new cars for the fleet.
Phoning round 64 car dealers, the mean quoted price for the 20 cars is £250,000 with a sample
standard deviation of £750. The best price you have been quoted is £2500 below the sample mean.
a) Should you take this offer or spend more time looking?
b) Determine the answer using a p-value. At what significance level would you reject the Null
hypothesis?
Question 3. A commonly used drug for treating COVID-19 is believed to be only 60% effective.
Experimental trials with a new drug administered to 100 affected adults showed that 70%
experienced less severe long COVID symptoms. Is the new drug more effective than the previous
one?
R questions
Question 1. This is an example how to create a function in R which performs a two-sided hypothesis
test of means in large samples
##Function for two-tailed hypothesis test in large samples
set.seed(9)
z.hyptest.twotail = function(muhyp,n,xbar,s,alpha) {
zstar = qnorm(1-alpha/2)
SE = s/sqrt(n)
teststat = (xbar-muhyp)/SE
p = 1-pnorm(teststat)
print(“critical value:”)
print(zstar)
print(“test statistic:”)
print(teststat)
print(“p-value:”)
print(p)
if ((teststat>=-zstar) & (teststat<=zstar)) {
print (“do not reject H0”)
}
else {
print (“reject H0”)
}
}
a. Test the hypothesis from seminar question 1 again using R
b. Now create a RV x from a sample with n=1000, drawn from a population with mean 530 and
standard deviation 90, and adapt the function to test the hypothesis that the population mean is
525. What do you decide?
c. Now create a new RV y with n=35, drawn from a population with mean 530 and standard
deviation 90. Test the hypothesis that the population mean is 525 again.
d. Create a function that performs one-sided hypothesis tests of means (again, by varying the
function defined at the beginning)
e. Draw a sample of n=64 from a population with mean 25000 and standard deviation 750. Test the
one-sided hypothesis in seminar question 2 again. What do you decide? Is this the correct
decision or are you making an error? If yes, which type of error?
