Question 1:- A potential investor collected attendance data over a period of 49 days at the North Mall and South Mall theaters in order to determine the difference between the average daily attendances. The North Mall Theater averaged 720 patrons per day with a variance of 100, while the South Mall Theater averaged 700 patrons per day with a variance of 96. Develop an interval estimate for the difference between the average daily attendances at the two theaters. Use a confidence coefficient of 0.95.

Question 2:-Zip, Inc. manufactures Zip drives on two different manufacturing processes. Because the management of this company is interested in determining if process 1 takes less manufacturing time, they selected independent random samples from each process. The results of the samples are shown below. (20 points)

                                          Process 1          Process 2

Sample size                               27               22

Sample mean (in minutes) 10              14

Sample variance                 16             25

1. State the null and alternative hypotheses.

2. Determine the degrees of freedom for the t-test.

3. Compute the test statistic

4. At 95% confidence, test to determine if there is sufficient evidence to indicate that process 1 takes a significantly shorter time to manufacture the Zip drives.

Question 3:-  

Shown below is a portion of computer output for a regression analysis relating to Y (dependent variable) and X (independent variable). (20 points)

ANOVA     

                  df SS

Regression   1 115.064

Residual 13   82.936

Total    

            Coefficients Standard Error

Intercept 15.532                 1.457

x              -1.106               0.261

a. Perform a t-test using the p-value approach and determine whether x and y are related. Let α = .05.

b. Using the p-value approach, perform an F test, and determine whether x and y are related.

c. Compute the coefficient of determination and fully interpret its meaning. Be specific.

A shingle of dimensions a = 12 inch ✕ b = 24 inch has to withstand the lift force created by winds of up to 86 miles per hour. (Density of air = 1.2 kg/m3

If we wish to map an area 3.1 miles × 500 feet with 2-foot contours, (Photo scale is 1″= 500 feet); how many photos are required to properly cover the area?

Exhibit L.1 reports the multivariate odds ratios comparing each category to women who never had an induced abortion and had at least one pregnancy. Researchers were able to interview 845 out of 1,011 (83.5 percent) of the eligible cases and 961 out of 1,239 (78 per- cent) of the eligible controls. Of the cases, only 689 (81.5 percent) had complete information on abortion history, compared to 781 (81.3 per- cent) of the eligible controls.

Note: 1. Estimated from the data. 2. Multivariate OR adjusts for age, family history of breast cancer, religion, age at first pregnancy. 3. Both crude and multivariate odds ratio estimates risk relative to women with a least one pregnancy who never had an induced abortion. Source: Daling et al. (1994).

Calculate the crude odds ratios for each of the abortion history strata in Exhibit L.1. What is the overall increased risk of abortion after adjusting for several covariates?

Given the following linear optimization model, transform this model into the required form and solve using Solver.

Objective function: 8.2? + 7.0? + 6.5? + 9.0? = ??????? ????

Constraints: 6? + 2? + 5? + 7? ≥ 820

?/? + ? + ? + ? ≥ 0.3

? + ? ? + ? ≥ 0.2

? ≥ ? + D

Please Use Excel

Consider the following hypotheses.

Upper H0​: p≤0.25

Upper H1​: p>0.25

Given that p=0.3​, n=110​, and α=0.05 answer the following questions.

a. What conclusion should be​ drawn?

b. Determine the​ p-value for this test.

If a cylindrical steel pressure vessel has a 400-mm inner radius and 8-mm-thick walls. Find the change (mm) in the inner radius when the vessel is pressurized to 1.2 MPa. Use E = 200 GPa and v = 0.3 for steel.