Basic statistics for economics pdf

Thus 6 classes are recommended. Use for convenience. The crest of the distribution is in the up to class which contains the greater part or 20 of the 33 months. Thus 5 classes are recommended. A suggest interval size would be Outstanding Shares millions Number of Companies 0 up to 10 up to 8 up to 4 up to 1 up to 1 Total The number of outstanding shares range from 0 to 2 billion, with the largest number of companies 10 of 24 having less than million outstanding shares.

Only 2 companies have more than million shares. This data is qualitative and can be represented with either a bar chart or a pie chart.

Bar charts are preferred when the goal is to compare the actual amount in each category. LO Amount Balance 0 up to up to up to up to up to up to up to By far the largest part, nearly three-fourths of adjustable gross income in South Carolina is from wages and salaries. Dividends and IRAs each contribute roughly another ten percent to AGI with eight percent coming from business income pensions, social security, and other sources.

LO Hours Spent on Personal Computer per week Number of Individuals 0 up to 2 7 2 up to 4 11 4 up to 6 The interval should be at least Merrill Lynch financial advisors need to promote the importance of investing for retirement in this age group. There are 50 observations so the recommended number of classes is 6. However, there are several states that have many more farms than the others, so it may be useful to have an open ended class.

One possible frequency distribution is. Farms in USA Frequency 0 up to 20 14 20 up to 40 14 40 up to 60 10 60 up to 80 8 80 up to 3 or more 1 Total 50 Twenty-six of the 50 states, or 56 percent, have fewer than 40, farms. There is one state that has more than , farms. Brown, yellow, and red make up almost 75 percent of the candies. The other 25 percent is composed of blue, orange, and green. There are many choices and possibilities here. For example you could choose to start the first class at , rather than , The choice is yours!

Conclude that there has been a significant increase in the intent to watch the TV programs. These studies help companies and advertising firms evaluate the impact and benefit of commercials.

This would suggest not using the proportion of DJIA stocks going up on a daily basis as a predictor of the proportion of NYSE stocks going up on that day. We should conclude that Medicare spending per enrollee in Indianapolis is less than the national average. There is not a statistically significant difference between the National mean price per gallon and the mean price per gallon in the Lower Atlantic states.

The proportion of workers not required to contribute to their company sponsored health care plan has declined. There seems to be a trend toward companies requiring employees to share the cost of health care benefits. Statistical Inference about Means and Proportions with Two populations 7. The population mean duration of games in is less than the population mean in Management should be encouraged by the fact that steps taken in reduced the population mean duration of baseball games.

However, the statistical analysis shows that the reduction in the mean duration is only 3. The interval estimate shows the reduction in the population mean is 1. Additional data collected by the end of the season would provide a more precise estimate.

In any case, most likely the issue will continue in future years. It is expected that major league baseball would prefer that additional steps be taken to further reduce the mean duration of games.

With 6 degrees of freedom t. Conclude that there is a difference between the population mean weekly usage for the two media. A difference exists with system B having the lower mean checkout time. Simple Linear regression The agent's request for an audit appears to be justified.

The scatter diagram shows a linear relationship between the two variables. The least squares line does not provide a very good fit. Or: Using F table 1 degree of freedom numerator and 5 denominator , p-value is between. The residual plot leads us to question the assumption of a linear relationship between x and y. Even though the relationship is significant at the. Regression or correlation analysis can never prove that two variables are casually related.

The DJIA is not that far beyond the range of the data. Multiple Regression 5. No, it is 1. In part b it represents the marginal change in revenue due to an increase in television advertising with newspaper advertising held constant. But there is a huge increase in the Adjusted R-Squared, and both variables have low p-values in part b.

Hence we can expect better predictions from the 2-variable model. Note: The Minitab output is shown in Exercise 5 a. NOTE: These answers seem to imply that a variable whose p-value is above alpha should be dropped.

The Minitab output is shown below: Fit Stdev. Confidence interval estimate: Prediction interval estimate: The estimated regression equation did not provide a good fit. In fact, the p-value of. We see that Person is highly correlated with Months the sample correlation coefficient is -. The standardized residual plot is shown below.

There appears to be a very unusual trend in the standardized residuals. The Minitab output shown in part a did not identify any observations with a large standardized residual; thus, there does not appear to be any outliers in the data. The Minitab output shown in part a identifies observation 2 as an influential observation. Regression Analysis: Model Building 4. Since the linear relationship was significant Exercise 4 , this relationship must be significant.

Note also that since the p-value of. The fitted value is A portion of the Minitab output follows: The regression equation is Scoring Avg.

Decision Analysis 1. The decision to be made is to choose the type of service to provide. Instructor feedback regarding student performance is important. These will be helpful as students progress through the course and use new statistical techniques to further explore the data.

The ideal ending for these continuing data analytics exercises is a comprehensive report based on the analytical findings. We know that working with a statistics class to develop a very basic competence in data analytics is challenging. Instructors will be teaching statistics.

In addition, instructors will be faced with choosing statistical software and supporting students in developing or enhancing their computer skills. Finally, instructors will need to assess student performance based on assignments that include both statistical and written components.

Using a mentoring approach may be helpful.