# slide10 - Diff of Means Var known Null hypothesis Test...

This preview shows pages 1–5. Sign up to view the full content.

1 Diff of Means, Var known Null hypothesis: Test statistic: 0 1 2 0 : H µ µ = ∆ 1 2 0 0 2 2 1 2 1 2 X X Z n n σ σ − ∆ = + 2 Example Hermione hypothesizes that the tulips in her garden are, on average, 2 inches taller than the crocuses. By taking some measurements, she knows that her 28 tulips have an average height of 8 inches (and standard deviation 1.5), while the 33 crocuses have an average height of 5 inches (and standard deviation 1).

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
3 Questions I Test the hypothesis at the 5% level. What is the P-value? Give the 95% confidence interval for the difference in the two means. 4 Confidence Intervals The 100(1– α )% confidence interval on the difference of two means is: 2 2 2 2 1 2 1 2 1 2 2 1 2 1 2 2 1 2 1 2 x x z x x z n n n n α α σ σ σ σ µ µ + + +
5 Required Sample Size (a) For the two-sided alternate hypothesis with significance level α , the sample size n 1 = n 2 = n required to detect a true difference in means of with power at least 1– β is: 2 0 2 2 2 1 2 / ) ( ) )( z z ( n σ σ β α + + = 6 Required Sample Size (b) If variances are known, and sample sizes are equal, the required sample size to guarantee an error no more than E at 100(1– α ) percent confidence is: ( ) 2 2 2 1 2 z n E α σ σ = +

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
7 Questions II
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern