Assuming that the following sample of 10 numbers arise from a Normal
distribution with mean and standard deviation σ = 5.8, obtain, from
first principles, 95% and 99% confidence intervals for .
39.7 22.0 37.1 25.4 24.3 29.4 26.6 31.5 28.2 22.7
Evaluate a test statistic for the null hypothesis H0 : = 30 against
the two-sided alternative hypothesis H1 : = 30, and calculate the
corresponding p-value associated with H0. What are your conclusions
about H0?
distribution with mean and standard deviation σ = 5.8, obtain, from
first principles, 95% and 99% confidence intervals for .
39.7 22.0 37.1 25.4 24.3 29.4 26.6 31.5 28.2 22.7
Evaluate a test statistic for the null hypothesis H0 : = 30 against
the two-sided alternative hypothesis H1 : = 30, and calculate the
corresponding p-value associated with H0. What are your conclusions
about H0?
-
First calculate the sample mean, m=28.69 then the 95% CI for mu is
(m-1.96(5.8/sqrt(10),m+1.96(5.8/sqrt(10… 31.789) and the 99% CI is
same but with 2.576 instead of 1.96.
The test statistic is z*=(28.69-30)/(5.8/sqrt(10)=-0.7142
.If H1 is mu not=30 then the test is 2-tailed and the p-value is double
P(Z<-0.7142)= 0.475
Conclusion this that there is very little evidence that mu is not =30.
I hope you can stop raging now.
(m-1.96(5.8/sqrt(10),m+1.96(5.8/sqrt(10… 31.789) and the 99% CI is
same but with 2.576 instead of 1.96.
The test statistic is z*=(28.69-30)/(5.8/sqrt(10)=-0.7142
.If H1 is mu not=30 then the test is 2-tailed and the p-value is double
P(Z<-0.7142)= 0.475
Conclusion this that there is very little evidence that mu is not =30.
I hope you can stop raging now.