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## Statistics

Attempt all the problems.

Section-A

problem1) Last year television stations WXYZ’s share of 11pm news audience was approximately equal to 25%. Station’s management believes that present audience share is higher than last year’s 25% figure. In an attempt to substantiate this belief, station surveyed 400 11pm viewers and found that 146 watched WXYZ. Set up the null and alternative hypothesis and test the same at 5% level of significance. What is your conclusion?

problem2)  A retailer that sells home entertainment systems accumulated 10451 sales invoices during the previous year. The total of the sales amount on these invoices as claimed by the company is Rs.63,84,675. In order to estimate the true total sales for last year, an independent auditor randomly selects 350 of the invoices and determines the actual sales amounts by contacting the purchasers. The mean and standard deviation of the 350 samples sales amounts are Rs. 532 and standard deviation 168. Find the point and interval estimate given that a 95% confidence is required.  Do you think that the sales invoice claimed by the company is correct?

problem3) One of the problems on the Business Week subscriber study was, “In the past 12 months when travelling for business, what type of airline ticket did you purchase most often”. The data obtained are shown in the following table.

Type of Flight
Type of Ticket                          Domestic flights    International flights
First Class                                           29                    22
Business / Executive class                   95                   121
Full fare economy /coach class            518                 135

Based on the above can it be concluded that type of ticket is dependent on the type of flight taken. Use 5% level of significance.

problem4) To study effect of temperature on yield in a chemical process, five batches were produced at each of three temperature levels. The results follow. Construct an analysis of variance table. Use a 5% level of significance to test whether the temperature level has an effect on the mean yield of the process.

Yield
Temperature
50degC         34    24    36    39    32
60degC         30    31    34    23    27
70degC         23    28    28    30    31

SECTION-B

Case Study

A research project was undertaken to determine if there is relationship between the years of experience on the job (A) and efficiency rating of employees (B). The purpose of the study was to predict the efficiency rating of the employee. The sample results are as follows:

Years of Job (A)         1    20    6    8    2    1    14    8    4    6
Efficiency rating (B)     6    5     3    5     2    2     4     3    3    4

a) Which variable is the dependent variable?

b) Find if there is correlation between the two variables and test the correlation coefficient. (Use 5% level of type I error)

c) Estimate the linear regression model. Do you think that the regression coefficient will be significant at 5% level of significance? Give reasons.

d) Do you think overall regression model will be significant. Give reasons.

Statistics and Probability, Statistics

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