Explain the purpose of applying multiple regression analysis. Following table shows the scores ($Y$) made by ten assemblies –line employees on a test design to measure the job satisfaction. It also shows the scores made on an aptitude test (X1​) and number of days absent (X2​) during the past year (excluding vacation).

i) Find the multiple regression equation for the sample data.
ii) Interpret the value of regression coefficients b₁ and b₂.
iii) Estimate the score of an employee whose aptitude test score is 9 and number of absent days are 6.

A management consulting company presents a 3-day seminar on project management to various clients. The seminar is basically the same each time it is given. However, sometimes it is presented to high-level managers, sometimes to mid-level managers, and sometimes to low-level managers. The seminar facilitators believe evaluations of the seminar may vary with the audience. Suppose the following data are some randomly selected evaluation scores from different levels of managers after they have attended the seminar. The ratings are on a scale from 1 to 100, with 100 being the highest score. Use a one-way ANOVA to determine whether there is a significant difference in the evaluation according to manager level. The following table gives the scores to the various clients due to different manager levels.

Explain, stating clearly the assumptions involved in the t-test for testing the significance of difference between two sample means. Measurements of the left-and-right-hand gripping strengths of 8 left-handed writers are recorded:

Do the data provide strong evidence that the people who write with left hand have greater gripping strength in the left hand than they do in the right hand? Use α=0.05.

What do you understand by design of experiments? Give the layout of a Latin Square Design. Explain why the number of treatments tested in a Latin Square Design should not be less than 3?

Based on interviews of couples seeking divorce, a social worker complies the following data related to the period of acquaintanceship before marriage and the duration of marriage:

Perform a test to determine if the data substantiate an association between the duration of a marriage and the acquaintanceship prior to marriage. Use 5% level of significance.

Define confidence level in estimation. A quality control inspector collected a random sample of 400 tubes of toothpaste from the production line and found that 20 of the tubes had leaks from the tail end. Construct 96% confidence interval for the percentage of all the toothpaste tubes that had leakage and interpret the result.

The mean drying time of a brand of spray paint is known to be 122 seconds. The research division of the company that produces this paint contemplates that adding a new chemical ingredient to the paint accelerate the drying process. To investigate this conjecture, the paint with the chemical additions is sprayed on 50 surfaces and the drying time is recorded. The mean and standard deviation of drying time computed from these recorded are found as 116 seconds and 16.8 seconds respectively. Do these data provide strong evidence that the mean drying time is reduced by the addition of the new chemical? Use 5% level of significance. Also find p-value.

Explain the concept of multiple and partial correlation coefficients. Consider three variables X1, X2​ and X3​. If

r ₁₂=0.40, r ₂₃=0.50 and r₁₃ =0.6  find R₁₂₃ and r_234.​

Discuss the concept of level of significance in hypothesis testing. A manufacturer of laptop provides a particular model in one of three colors. Of the first 100 laptops sold, it is noted that 80 were the first color. Can you conclude that more than two third of all the customers have a preference for the first color? Use 5% level of significance.

A multiple regression equation yields the following results:

i) What is the total sample size?
ii) How many independent variables are being considered?
iii) Compute the coefficient of determination and interpret its value.
iv) Compute the standard error of estimate.
v) Test the hypothesis that the overall fit of the model is significant or not. Assume α=0.05.

Explain briefly the queuing theory. Customers arrive at a one-man barber shop according to Poisson process with mean inter arrival time of 12 minutes. Customer spends an average of 10 minutes in the barber’s chair. What is the expected number of customers in the barber shop in the queue?

Write short note on:
a) Central limit theorem.
b) Determination of required sample size to estimate population proportion.