You are given the following information obtained from a random sample of 5 obser

Question

You are given the following information obtained from a random sample of 5 observations. 20 18 17 22 18 At a 10% level of significance, determine whether or not the mean of the population from which this sample was taken is significantly less than 21. (Assume the population is normally distributed.) You are given the following information obtained from a random sample of 5 observations. 20 18 17 22 18 At a 10% level of significance, determine whether or not the mean of the population from which this sample was taken is significantly less than 21. (Assume the population is normally distributed.) 20 18 17 22 18 At a 10% level of significance, determine whether or not the mean of the population from which this sample was taken is significantly less than 21. (Assume the population is normally distributed.)

Explanation / Answer

here sample mean=Xbar=19     sample SD=S=2      sample size=n=5

here null hypothesis H0=population mean=mu=21         and alternative hypothesis H1=population mean=mu<21

here alpha=0.10

test statistic is T=(Xbar-mu)*sqrt(n)/s which under H0 follows a t distribution with degrees of freedom 5-1=4

so we reject h0 iff observed value of T=t<t4,alpha=0.1   where t4,alpha=0.1 is the upper 0.1 point of a t distribution with 4 degrees of freedom

now observed value of t is (19-21)*sqrt(5)/2=-2.236

and t4,alpha=0.1=1.53321

so -2.236<1.53321

hence we reject H0 and conclude that the mean of the population from which this sample was taken is significantly less than 21.

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