Consider the problem in Exercise 1 again. The company wants to conduct a test, w

Question

Consider the problem in Exercise 1 again. The company wants to conduct a test, with a = 0.05, to see whether the fleet average is less than 26 mpg. Which kind of tests is appropriate to use here, z-test or t-test? Write appropriate hypotheses. Is the alternative hypothesis one-sided or two-sided? Use R to compute the test statistic and construct rejection region. Make conclusion using the test statistic and rejection region. Use R to compute p-value. Make conclusion using p-value. Is it consistent with the conclusion in part (c)?

Explanation / Answer

Since standard deviation is not given so we cannot use z-test and hence I will assume that our sample size is less than 30 (i.e n<30) to apply a t-test.

Now following will be our null and alternative hypothesis:
Null hypothesis, H0: mu = 26
Alternative hypothesis, Ha: mu<26
Type of hypothesis test : Left tailed, directional

computing test statistics in R:
fleet <- read.table("path of the file", header=TRUE, sep=" ") # I assume that delimiter of the file is tab separated
   # and file has header row
#then r has a function t.test which directly computes test statistics as follows
t.test(fleet, mu=26, alternative="less", conf = 0.95) #this will give us p-value
#if p-value is greater than alpha(i.e 0.05) than we fail to reject null hypothesis in favour of the alternative hypothesis or vice-versa.

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