On March 11, 2011, Japan was struck by a magnitude-8.9 earthquake off its northe

Question

On March 11, 2011, Japan was struck by a magnitude-8.9 earthquake off its northeastern coast. This natural disaster halted production in many Japanese industries as many firms were inoperable for several weeks and months. Given a firm’s stock price is based on the present value of future cash flows, its stock price will vary depending on whether investors believe the firm is expected to continue to produce and sell its product, and thus, have cash flows.

Using “Toyota’s stock price” tab of the assignment 2 Excel file on Canvas, conduct a comparative analysis that tests the hypothesis that Toyota’s post-earthquake stock price (e.g., 6 month time period March 11, 2011-September 12, 2011) is lower than its pre-earthquake stock price (e.g., 6 month time period September 10, 2010-March 10, 2011).

To successfully complete this problem, you must do the following:

Round answers to three decimal places.

Conduct an F-test to test if the variation in the stock price is the same in the two time periods (e.g., test that the variances are the same). Use your results from this test to conclude which t-test is appropriate to use (e.g., t-Test: Two-Sample Assuming Equal Variances or t-Test: Two-Sample Assuming Unequal Variances). In your answer, include all the steps of a hypothesis test.

Conduct the appropriate t-test to test if the average stock price is lower in the post-earthquake period compared to the pre-earthquake period. In your answer, include all the steps of a hypothesis test. ***Is this a one-tailed or a two-tailed test? How do you know?

Clearly interpret your results so that you draw a conclusion about whether or not Toyota’s stock price significantly dropped after the earthquake.

*Below is the excel data

Source: Tokyo Stock Exchange Date Stock Price at Close 9/10/10 70.6 9/13/10 70.29 9/14/10 69.8 9/15/10 71.22 9/16/10 71.73 9/17/10 71.51 9/20/10 72.18 9/21/10 71.63 9/22/10 71.55 9/23/10 70.97 9/24/10 73.06 9/27/10 72.4 9/28/10 73.15 9/29/10 73 9/30/10 71.58 10/1/10 71.8 10/4/10 70.79 10/5/10 72.03 10/6/10 71.19 10/7/10 71.15 10/8/10 71.07 10/11/10 70.87 10/12/10 70.05 10/13/10 70.3 10/14/10 72.37 10/15/10 71.51 10/18/10 72.58 10/19/10 71.35 10/20/10 71.69 10/21/10 71.62 10/22/10 71.7 10/25/10 71.36 10/26/10 70.87 10/27/10 70.91 10/28/10 71.13 10/29/10 70.82 11/1/10 69.63 11/2/10 70.23 11/3/10 70.71 11/4/10 72.73 11/5/10 72.64 11/8/10 73.74 11/9/10 73.1 11/10/10 75 11/11/10 75.25 11/12/10 75.51 11/15/10 75.66 11/16/10 74.93 11/17/10 75.85 11/18/10 77.29 11/19/10 78.47 11/22/10 78.47 11/23/10 77.43 11/24/10 78.93 11/26/10 78.36 11/29/10 78.25 11/30/10 77.69 12/1/10 79.58 12/2/10 79.02 12/3/10 79.05 12/6/10 79.14 12/7/10 78.67 12/8/10 78.36 12/9/10 77.97 12/10/10 77.26 12/13/10 77.98 12/14/10 78.04 12/15/10 78.14 12/16/10 78.3 12/17/10 77.48 12/20/10 77.23 12/21/10 78.01 12/22/10 77.69 12/23/10 77.66 12/27/10 77.9 12/28/10 78.25 12/29/10 79.1 12/30/10 78.35 12/31/10 78.63 1/3/11 79.43 1/4/11 79.86 1/5/11 80.2 1/6/11 81.54 1/7/11 82.46 1/10/11 82.77 1/11/11 83.38 1/12/11 84.44 1/13/11 85.39 1/14/11 85.96 1/18/11 85.18 1/19/11 84 1/20/11 83.36 1/21/11 82.01 1/24/11 83.5 1/25/11 83.86 1/26/11 82.29 1/27/11 83.53 1/28/11 81.36 1/31/11 82.18 2/1/11 83.29 2/2/11 85 2/3/11 84.68 2/4/11 84.75 2/7/11 85.13 2/8/11 88.57 2/9/11 89.63 2/10/11 88.82 2/11/11 90.05 2/14/11 92.81 2/15/11 92.97 2/16/11 93.68 2/17/11 93.45 2/18/11 93.2 2/22/11 90.69 2/23/11 90.17 2/24/11 90.1 2/25/11 91.75 2/28/11 93.3 3/1/11 92.84 3/2/11 91.53 3/3/11 92.19 3/4/11 90.99 3/7/11 89.02 3/8/11 89.99 3/9/11 89.54 3/10/11 87.52 3/11/11 85.65 3/14/11 81.73 3/15/11 81.39 3/16/11 80.41 3/17/11 82.06 3/18/11 81.56 3/21/11 83.75 3/22/11 83 3/23/11 82.14 3/24/11 81.19 3/25/11 80.76 3/28/11 80.55 3/29/11 79.71 3/30/11 80.96 3/31/11 80.25 4/1/11 80.51 4/4/11 79.48 4/5/11 77.63 4/6/11 77.35 4/7/11 77.21 4/8/11 77.88 4/11/11 76.5 4/12/11 77.2 4/13/11 77.98 4/14/11 77.88 4/15/11 77.64 4/18/11 77.25 4/19/11 76.12 4/20/11 77.26 4/21/11 77.8 4/25/11 79.51 4/26/11 78.66 4/27/11 78.29 4/28/11 79.5 4/29/11 79.68 5/2/11 80.16 5/3/11 79.69 5/4/11 79.76 5/5/11 79.56 5/6/11 79.1 5/9/11 79.36 5/10/11 81.02 5/11/11 81.46 5/12/11 83.63 5/13/11 83.38 5/16/11 82.21 5/17/11 81.37 5/18/11 81.39 5/19/11 80.7 5/20/11 79.96 5/23/11 79.54 5/24/11 79.89 5/25/11 81.77 5/26/11 82.21 5/27/11 82.26 5/31/11 83.29 6/1/11 81.5 6/2/11 80.91 6/3/11 80.51 6/6/11 79.92 6/7/11 81.57 6/8/11 81.75 6/9/11 81.92 6/10/11 80.67 6/13/11 79.72 6/14/11 80.44 6/15/11 79.48 6/16/11 79.47 6/17/11 79.51 6/20/11 80.13 6/21/11 80.76 6/22/11 80.7 6/23/11 80.82 6/24/11 81.29 6/27/11 79.74 6/28/11 80.08 6/29/11 81.53 6/30/11 82.42 7/1/11 83.45 7/5/11 83.6 7/6/11 84.27 7/7/11 84.64 7/8/11 84.4 7/11/11 83.7 7/12/11 83.64 7/13/11 84.68 7/14/11 84.28 7/15/11 83.85 7/18/11 83.36 7/19/11 84.24 7/20/11 84.33 7/21/11 85.47 7/22/11 85.01 7/25/11 84.13 7/26/11 84.1 7/27/11 82.17 7/28/11 81.43 7/29/11 81.92 8/1/11 81.77 8/2/11 81.29 8/3/11 81.26 8/4/11 77.41 8/5/11 77.43 8/8/11 73.72 8/9/11 77.21 8/10/11 73.43 8/11/11 75.14 8/12/11 74.4 8/15/11 76.12 8/16/11 75.42 8/17/11 74.68 8/18/11 71.57 8/19/11 70.7 8/22/11 70.54 8/23/11 72.88 8/24/11 72.08 8/25/11 71.27 8/26/11 71.65 8/29/11 72.1 8/30/11 70.94 8/31/11 71.84 9/1/11 71.17 9/2/11 69.34 9/6/11 68.27 9/7/11 69.85 9/8/11 69.37 9/9/11 67.8 9/12/11 68.17

Explanation / Answer

Solution:

First enter Data in R

> postearthquake= scan("clipboard")

Read 128 items

> preearthquake= scan("clipboard")

Read 126 items

H0:    12 = 22 Vs H1 :  12 22

R out put

> var.test(postearthquake,preearthquake)

        F test to compare two variances

data: postearthquake and preearthquake

F = 0.35372, num df = 127, denom df = 125, p-value = 1.16e-08

alternative hypothesis: true ratio of variances is not equal to 1

95 percent confidence interval:

0.2490019 0.5022423

sample estimates:

ratio of variances

         0.3537247

Here p-value = 1.16e-08 is less than 0.05 .Therefore we reject H0. Therefore we can conclude that the variation in the stock price is not same in the two time periods i.e. postearthquake and preearthquake .

b) Now we test the hypothesis that Toyota’s post-earthquake stock price (e.g., 6 month time period March 11, 2011-September 12, 2011) is lower than its pre-earthquake stock price (e.g., 6 month time period September 10, 2010-March 10, 2011).

      For this we use t test : two sample assuming unequal variance.

       Here

                  H0:    µ1 = µ2 Vs H1 : µ1 < µ2

> t.test(postearthquake,preearthquake,aleternative="less")

        Welch Two Sample t-test

data: postearthquake and preearthquake

t = 0.26077, df = 202.98, p-value = 0.7945

alternative hypothesis: true difference in means is not equal to 0

95 percent confidence interval:

-1.259967 1.644035

sample estimates:

mean of x mean of y

79.20687 79.01

Here p-value is 0.7945 which is greater than 0.05. Therefore we accept H0. We conclude that

Toyota’s post-earthquake stock price (e.g., 6 month time period March 11, 2011-September 12, 2011) and pre-earthquake stock price (e.g., 6 month time period September 10, 2010-March 10, 2011) are same.

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