Does the evidence suggest that the volume of Apple stock has changed since 2007?
ID: 3227108 • Letter: D
Question
Does the evidence suggest that the volume of Apple stock has changed since 2007? Use the a = 0.05 level of significance. Volume of Google Stock Google became a publicly traded company In August 2004. Initially, the stock traded over 10 million shares each day! Since the Initial offering, the volume of stock traded daily has decreased substantially. In 2007. the moan daily volume in Google stock was 5.44 million shares, according to Yahoo! Finance. A random sample of 35 trading days in 2010 resulted in a sample mean of 3.28 million shares with a standard deviation or 1.68 million shares. (a) Based on the histogram and boxplot shown (from StatCrunch), why is a large sample necessary to conduct a hypothesis test about the mean? (b) Does the evidence suggest that the volume of Google stock has changed since 2007? Use the alpha = 0.05 level of significance. Using Confidence Intervals to Test Hypotheses Test the hypotheses in Problem 23 by constructing a 99% confidence interval. Using Confidence Intervals to Test Hypotheses Test the hypotheses in Problem 24 by constructing a 95% confidence interval. Using Confidence Intervals to Test Hypotheses Test the hypotheses in Problem 25 by constructing a 95% confidence interval. Using Confidence Intervals to Test Hypotheses Test the hypotheses in Problem 26 by constructing a 95% confidence interval. Statistical Significance versus Practical Significance A math teacher claims that she has developed a review course that increases the scores of students on the math portion of the SAT exam. Based on data from the College Board, SAT scores are normally distributed with mu = 515. The teacher obtains a random sample of 1800 students.Explanation / Answer
(a) The standard deviation of shares traded = 1.68 million
Mean shares traded in 2010 = 3.28 million shares
If we take the mean/standard deviation ratio, 3.28/1.68 = 1.95, which shows that the data has high standard deviation and widely distributed across the mean. This can also be seen in the histogram and boxplot. The sample size is proportional to the square of the standard deviation. As the standard deviation is high, the sample size should be large to conduct the hypothesis test.
(b) Mean shares traded in 2007 = 5.44 million shares
Standard error of the mean shares traded = 1.68/sqrt(35) = 0.284
t = (5.44 - 3.28) /0.284 = 7.6
Critical value of t at alpha = 0.05 is 1.69
As, observed t-value (7.6) is greater than the critical value (1.69), we reject the null hypothesis and conclude that the average shares traded changed from 2007 to 2010.
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