statstics

21. What is the Significance level?

22. When should the z-test and the t-test be used?

24. Work on problem number 14 of page 10-30 and answer the following questions below.

b) Calculate 𝑠2 𝑒	22 c) What is 𝑠𝑒 , the square root of 𝑠𝑒 , called? What is its value in the case?
d) ***Assume ei = 0 at α = 0.05 At the predicting Y| X = 4, and find the confidence interval for this 𝑌 ̂
e) Estimating μY| X =4
f) Describe in about 5-6 sentences what you got the result from d) and e)?

25. Consider the following hypothesis test

H0: μ = 15

H0: μ >15

A sample of 40 provides a sample mean of 16.5 and sample standard deviation of 7.

a) Using α = 0.2, what is the critical value of z? What is the rejection rule?

b) Compute the value of the test statistic z.

c) What is the p-value?

d) What is your conclusion?

26. n=27, 𝑋=128.4, S=20.6 what is the 98% confidence interval for μ at 98%.

From ∝ = 1-0.98=0.02

27

b. Compute F and test at 0.05 level of significance to see whether a significant relationship is present

c. Did the estimated regression equation provide a good fit to data? Explain

d. Use the t-test and alpha = 0.05 to test H0: B1=0 and H0: B2=0

28. A large hotel purchased 200 new color televisions several months ago: 80 of one brand and 60 of each of two other brands. Records were kept for each set as to how many service calls were required, resulting in the table that follows.

Assume that TV sets are random samples of their brands. With 5% risk of Type I error, test for an association between TV brand and the number of service calls.

Is the X2 value significant at 5% level of significant? Write the conclusion for this question.

H0: TV brand and the number of service calls are independent Ha: Two of criteria of these are dependent

29. A regression model relating X, number of salesperson at a branch office, to y, annual sales at the office ($1000s), has been developed. The computer output from a regression analysis of the data follows.

.

a) Write the estimated regression equation

b) How many branch offices were involved in the study?

c) Compute the F statistic and test the significance of the relationship at a .05 level of significance.

d) Predict the annual sales at the Memphis branch office. This branch has 12 salespersons.

e) Test the null B1=0 against the B1>0 (alpha = 0.05)

30. Answer the following questions: a) If r2 = 0.95, n=11 and the ∑(𝑦 − 𝑦̅)2 = 100,what is 𝑠2𝑜𝑟 𝑠2 ?

b) If r2 = 1, then 𝑠2 in (45a) can be shown to have what type of relationship with SST 𝑒

and SSR?

c) What relationship exists between 𝑦̂ and Y where r2 = 1?

d) What relationship exists between 𝑦̂ and Y where r2 = 0?

e) Given the following information: r2 = 0.95, n = 10 and k = 2 what is the t-value for b1?

f) In (e), you calculated t-value at the 0.05 level of significance; what statistical decision can you make about b1?

a) What is sample size?

b) Write the estimated regression equation

c) What’s the sample regression coefficient of b0

d) What’s the sample regression coefficients of b2

e) What’s the value of the estimated variance of the regression

f) What’s the value of the standard error of the regression

g) What’s the value of the estimated variance of the b2

h) What’s the value of the standard error of the b2

i) Is the result significant when using F statistic to test the significant of the relationship at a 0.05 level of significance?

a) Compute the sample regression coefficients b0 and b1.

2. b)  Compute the estimated variance of the regression and the standard error of the regression.

3. c)  Compute the estimated variance of b1.

4. d)  Compute the standard error of b1.

5. e)  Test the slope coefficient using the alternative hypothesis of greater than zero and alpha = 0.01

6. f)  What is the F value?