What Is a Standard Error - Term Paper Example

Marketing and Statistics 1. a. What is a standard error? The term standard error refers to the standard deviation of the probability distribution of a statistic of interest from a random sample. b. What is statistical inference? Statistical inference is the process of drawing conclusions from the information available about a statistic of interest. c. Why is the standard error a central concept in statistical inference, and always necessary to know before doing inference? In pursuing statistical inference, we state the null hypothesis, a proposition of our point of interest in the study. The standard error indicates the expected error in the sample from which the inference is to be drawn.   Consider the following item from your survey, Learn2_4: To be properly educated, I should understand some real world applications of statistics, such as in marketing research. A 0 is maximum disagree and a 100 is maximum agree.   Consider the following item from your survey, Learn2_3:  I am only taking this class because it is required. A 0 is maximum disagree and a 100 is maximum agree.     2.  Compare the responses to Learn2_3 and Learn2_4. a. Compare the histograms and comment.   Diagram 1 is the histogram of learn2_3. It is fairly bell-shaped. This is an indication that the data are normally distributed. Thus, the distribution of those with a strong agreement to the opinion that they attend the class just as a requirement is normal. We expect the mean, mode, and median for this group to be centered close together. Diagram 2 is the histogram of learn2_4. A glance at it shows extreme skewness to the left. Most of the data points fall left of the mean. Therefore the respondents’ distribution on the opinion that” they should understand some real-world applications of statistics, such as in marketing research in order to be properly educated” is representative of a majority of ‘strongly agrees’. b. Compare the sample standard deviations and comment. Std. dev. Learn2_3: 29.397 Std. dev. Learn2_4: 22.183 Learn2-3 has a higher standard deviation, implying that it also has a higher standard error. More precisely, the deviation from the mean is higher than that of respondents who answered the ‘attendance as a necessity’ question. c. Relate the histograms to the respective standard deviations. The normal distribution of respondents who attend statistics classes as a requirement contributes to the huge spread of values on either side of the mean, creating a higher standard deviation. The histogram of learn2-4 is skewed to the left. It corresponds to the lower standard deviation, indicating little variation from the extremely right-placed mean on the histogram.   3. Consider Learn2_4. Responses above 50 indicate Agreement and below 50 indicate Disagreement.  Is the mean population response in the Agreement or Disagreement region? (Note: The two questions on the smd do not apply here. Also, there is no grouping variable, so that part of the questions is ignored as well.) It lies in the Agreement region. The mean respondent score lies close to the most frequent answer to the question, that the respondent strongly agrees they are learning statistics for proper education and understanding of the statistical application.   4. Compare Gender, men and women students, on Learn2_4. Is there a difference in the population means of men and women in this class? Let 2 represent female students. Then they are 12. The number of men is 17, with one undetermined case. Females: 870/12=72.5=μ1 Males: 1523/18=84.61=μ2 H0: μ1= μ2 H: μ2≠ μ2 ANOVA    Source of Variation SS df MS F P-value F crit Between Groups 1056.089 1 1056.089 3.915958 0.057741 4.195972 Within Groups 7551.278 28 269.6885    Total 8607.367 29     P-value>level of significance that is 0.05774>0.05. Therefore we accept the null hypothesis and conclude that there is no significant difference in the means.   5. Compare Gender, men and women students, on Learn2_3. Is there a difference in the population means of men and women in this class? H0: μ1= μ2 H: μ2≠ μ2   ANOVA               Source of Variation SS df MS F P-value F crit   Between Groups 638.45 1 638.45 0.759922 0.390767 4.195972   Within Groups 23524.25 28 840.1518   P-value<level of significance, thus we reject the null hypothesis. The means are significantly different. Read More