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General electric stock volume Example 7 analyzed the trading volume of shares of General Electric stock between February and April 2011. Summary statistics of the data were calculated using MINITAB and are shown below: The \(95 \%\) confidence intervals for the means are \((40.2685 .\) 63.3679 ) for Monday's volume and (42.7963,57.2037) for Friday's. Interpret each of these intervals, and explain what you learn by comparing them.

Short Answer

Expert verified
Both intervals indicate the average trading volume, with Monday's being more variable. No significant difference between Mondays and Fridays.

Step by step solution

01

Understand Confidence Intervals

A confidence interval is a range of values, derived from a data set, that is likely to contain the value of an unknown population parameter. The confidence level represents the percentage of intervals that would contain the parameter if you drew many samples. A 95% confidence interval indicates that if we were to take 100 different samples and compute a confidence interval for each sample, then approximately 95 of the intervals will contain the mean volume.
02

Interpret Monday's Confidence Interval

The confidence interval for Monday's trading volume is (40.2685, 63.3679). This means we are 95% confident that the average volume of shares traded on Mondays falls between 40.2685 and 63.3679 units (in thousands or millions depending on the data's unit). It represents the range in which the true average volume likely lies for the entire population of Monday trading volumes.
03

Interpret Friday's Confidence Interval

The confidence interval for Friday's trading volume is (42.7963, 57.2037). This indicates that we are 95% confident that the average trading volume on Fridays falls between 42.7963 and 57.2037 units. Like Monday's interval, this reflects the range in which the true average volume for the population is likely to be found.
04

Compare the Intervals

By comparing the intervals for Monday and Friday, you can see Monday's interval (40.2685 to 63.3679) is slightly broader and starts lower than Friday's interval (42.7963 to 57.2037). This suggests that Monday's trading volume could potentially be more variable. The overlap in the intervals implies there is no significant difference in the average trading volume between these two days at a 95% confidence level.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Trading Volume Analysis
Trading volume analysis involves examining the number of shares traded over a specific period. For companies like General Electric, understanding trading volume can provide insights into market activity and investor interest. A higher trading volume often indicates increased investor activity, which could be driven by news events, earnings announcements, or broader market trends. When analyzing trading volumes, we typically look for patterns or irregularities that might suggest a change in investor sentiment. For example, a significant spike in trading volume might signal that investors anticipate a company's stock price will move substantially. Thus, trading volume analysis is a vital tool for investors and market analysts to predict price movement and make informed investment decisions.
Population Parameter Estimation
Population parameter estimation involves using sample data to estimate characteristics or parameters of a larger population. In the context of the trading volume of General Electric stock, the "population" refers to the total trading volume of shares for all Mondays and Fridays during the observed period. A confidence interval gives us a range of values within which we expect the true population parameter to lie. For example, the confidence interval for Monday's trading volume indicates where the true average Monday trading volume probably falls based on our sample data. This method is essential in statistical analysis because it allows us to make predictions about a large population from a limited data set without analyzing every single data point.
Statistical Interpretation
Statistical interpretation requires understanding what confidence intervals signify about a data set. A confidence interval of 95% suggests that if repeated samples were taken, 95 out of 100 times, the interval would contain the true mean trading volume. This does not mean there is a 95% probability the true mean lies within this interval—the interval either contains the mean or it does not. In the case of General Electric, interpreting the intervals for both Mondays and Fridays helps us understand the likely range for average trading volumes. By statistically interpreting these intervals, analysts ascertain the reliability and stability of the observed trading volumes, assisting in future market strategies and predictions.
Data Variability Comparison
Data variability comparison involves analyzing the spread of data points in a given set. In the context of the exercise, the confidence intervals for trading volumes on different days show variability in the data. Comparing Monday's broader confidence interval to Friday's, we can infer that Monday's trading volume might be more variable. The overlap between Monday’s and Friday’s confidence intervals suggests no significant difference in their average trading volumes. This indicates that although there is variability, it is not substantial enough to claim a definitive difference in trading activity between these days. Evaluating variability is crucial for identifying consistency or volatility in trading patterns, providing insight into how a stock is performing over time.

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Most popular questions from this chapter

Psychologists' income In \(2003,\) the American Psychological Association conducted a survey (at research.apa.org) of a random sample of psychologists to estimate mean incomes for psychologists with various academic degrees and levels of experience. Of the 31 psychologists who received a masters degree in \(2003,\) the mean income was \(\$ 43,834\) with a standard deviation of \(\$ 16,870\) a. Construct a \(95 \%\) confidence interval for the population mean. Interpret. b. What assumption about the population distribution of psychologists' incomes does the confidence interval method make? c. If the assumption about the shape of the population distribution is not valid, does this invalidate the results? Explain.

\(m\) and \(n\) Consider the sample size formula \(n=\left[\hat{p}(1-\hat{p}) z^{2}\right] / m^{2}\) for estimating a proportion. When \(\hat{p}\) is close to 0.50 , for \(95 \%\) confidence explain why this formula gives roughly \(n=1 / m^{2}\).

Alleviate PMS? A pharmaceutical company proposes a new drug treatment for alleviating symptoms of PMS (premenstrual syndrome). In the first stages of a clinical trial, it was successful for 7 out of 10 women. a. Construct an appropriate \(95 \%\) confidence interval for the population proportion. b. Is it plausible that it's successful for only half the population? Explain.

U.S. popularity In \(2007,\) a poll conducted for the \(\mathrm{BBC}\) of 28,389 adults in 27 countries found that the United States had fallen sharply in world esteem since 2001 (www globescan.com). The United States was rated third most negatively (after Israel and Iran), with \(30 \%\) of those polled saying they had a positive image of the United States. a. In Canada, for a random sample of 1008 adults, \(56 \%\) said the United States is mainly a negative influence in the world. True or false: The \(99 \%\) confidence interval of (0.52,0.60) means that we can be \(99 \%\) confident that between \(52 \%\) and \(60 \%\) of the population of all Canadian adults have a negative image of the United States. b. In Australia, for a random sample of 1004 people, \(66 \%\) said the United States is mainly a negative influence in the world. True or false: The \(95 \%\) confidence interval of (0.63,0.69) means that for a random sample of 100 people, we can be \(95 \%\) confident that between 63 and 69 people in the sample have a negative image of the United States.

Women's satisfaction with appearance A special issue of Newsweek in March 1999 on women and their health reported results of a poll of 757 American women aged 18 or older. When asked, "How satisfied are you with your overall physical appearance?" \(30 \%\) said very satisfied, \(54 \%\) said somewhat satisfied, \(13 \%\) said not too satisfied, and \(3 \%\) said not at all satisfied. True or false: Since all these percentages are based on the same sample size, they all have the same margin of error.

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