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# Hypothesis Testing,Regression Analysis & Probability

1. If the daily stock price, x, of United Technology is normally distributed with mean 6.56 and standard deviation 2.4, calculate the probability that in a randomly selected ay the price will be between \$3.25 and \$7.36. Hint: Review normal distribution.

2. An industry is comparing its performance against an industry benchmark that no more than 30 percent of its product will be returned by its customers in a given month. A sample of 350 customers 113 of them returned the company product. At &#945; = .025, does this sample prove that the rate of return exceeds the benchmark?

Section-1 Section 2 Section 3 Section 4
The Appropriate test in this case is The Appropriate Null hypothesis is The Appropriate alternate hypothesis is The P-value hypothesis is
A Z A µ1 > 30% A µ1 &#8805; 30% µ2 A 0.18
B t B P1 = P2 B P1 &#8800; P2 B 0.05
C F C P = .3 C P > .3 C 0.93
D Chi-Square D None D None D None

3. Price and earning data of United Technology is given in the following table. Estimate the regression equation.

Price (Y) 20 23 25 27 23
Earning (X) 0.54 0.56 0.65 0.76 0.5

3. An important measure of the risk associated with a stock is the standard deviation, or variance, of the stock's price movements. A financial analyst wants to test the hypothesis that stock A has a greater risk than stock B. A random sample of 25 daily prices of stock A gives the sample variance of =6.52, and a random sample of 22 daily prices of stock B gives a sample variance of =3.47. Carry out the F-test at &#945; = 0.01.
There are four sections to this question, just choose the correct answers in each case

Section-1 Section 2 Section 3 Section 4
The Appropriate test in this case is The Appropriate Null hypothesis is The Appropriate alternate hypothesis is The P-value hypothesis is
A Z A µ > 25 A µ1 &#8805; µ2 A 1.59
B t B &#963;1 > &#963;2 B &#963;1 &#8800; &#963;2 B 2.05
C F C &#963;1 = &#963;2 C &#963;1 < &#963;2 C 0.05
D Chi-Square D None D None D 0.14

5. Following figures in millions are the sample sells figures of three difference branches of a company. Analyze the data.
Branch A Branch B Branch C
4.42 4.32 4.33
4.21 3.42 3.34
5.21 4.24 3.69
4.22 3.25 4.21
5.21 4.34 4.21
4.68 3.23 4.21
4.23 4.23 3.23

#### Solution Summary

The solution provides step by step method for the calculation of testing of hypothesis, regression equation and normal probability. Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.

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