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Older Siblings (Example 3) At a small four-year college, some psychology students were asked whether or not they had at least one older sibling. The table shows the results for men and women and shows some of the totals. \(\begin{array}{|lccc|} \hline & \text { Men } & \text { Women } & \text { Total } \\ \hline \text { Yes, Older S } & 12 & 55 & ? \\ \hline \text { No Older S } & 11 & 39 & 50 \\ \hline & 23 & ? & 117 \\ \hline \end{array}\) a. Calculate the totals that are not shown, and report them in the table. b. What percentage of the men had an older sibling? c. What percentage of the men did not have an older sibling? d. What percentage of the women had an older sibling? e. What percentage of the people had an older sibling? f. What percentage of the people with an older sibling were women? g. Suppose that in a group of 600 women, the percentage who have an older sibling is the same as in the sample here. How many of the 600 women would have an older sibling?

Step by step solution

01

Fill up the missing totals

First step is to fill in the missing values in the table. From the data, it can be seen that the total number of students is 117. According to the given table, there are already 50 students without older siblings counted. Subtract this from the total to find the number of students with older siblings. \(117 - 50 = 67\). So, there are 67 students with older siblings. Insert this into the 'Yes, Older S' row of the 'Total' column. For the total number in the 'Women' column, subtract the number of men from the total number of students. \(117 - 23 = 94\). So, insert 94 in the 'Women' column total.

02

Calculate the required percentages

Based on the filled table:a. The percentage of men who had an older sibling is \((12 / 23) * 100 = 52.17%\)b. The percentage of men who did not have an older sibling is \((11 / 23) * 100 = 47.83%\)c. The percentage of women who had an older sibling is \((55 / 94) * 100 = 58.51% \)d. The percentage of people who had an older sibling is \((67 / 117) * 100 = 57.26%\)e. The percentage of people with an older sibling who were women is \((55 / 67) * 100 = 82.09% \)

03

Calculate the number of women with an older sibling in the group of 600

Based on the percentage calculated before in step 2c, apply this percentage to the group of 600 women to get the number of women with an older sibling. So, \((58.51 / 100) * 600 = 350.14 \). Since you cannot have a fraction of a person, round this down to 350. So, out of 600 women, approximately 350 women have an older sibling.

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Key Concepts

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

Psychology Statistics

Understanding statistics is essential for psychology students as it allows them to analyze behavioral data effectively. Statistics in psychology help to quantify behaviors, measure variables, and ultimately give meaning to the numerical data collected during research. For instance, when surveys are conducted to understand the family dynamics among college students, as in our exercise, psychologists rely on statistical methods to process the raw data. They may explore the prevalence of certain family structures, such as having older siblings, and its potential impact on individuals. Here, knowing how to process and interpret data, like calculating totals and determining percentages, is crucial in drawing psychological conclusions and making inferences about a larger population based on sample data.

Percentage Calculation

Percentage calculation is a powerful tool for making comparisons and understanding ratios in a standard format. It is especially useful in statistical data analysis because it allows for the normalization of data, making it easier to compare different groups or categories. In the textbook exercise, we calculated the proportion of men and women with or without older siblings, converting these proportions into percentages to facilitate comparison. To calculate a percentage, the formula used is (Part / Whole) * 100. It is essential to ensure accuracy by correctly identifying the 'part' and 'whole' aspects of the data. For example, seeing that 58.51% of women in our sample have older siblings tells us more than just saying 55 out of 94 women—it provides a rate that can be compared across different groups or situations.

Statistical Inference

Statistical inference is the process of making deductions about a population based on sample data. It involves using probability to determine how likely it is that a certain statistic is a reliable reflection of the broader population. In our exercise, statistical inference is used to extrapolate findings from the college sample to a larger group of 600 women. Using the percentage of women with older siblings found in the sample, we infer that the same percentage would apply to the larger group. This approach is fundamental in research, allowing for predictions and the formulation of theories. Keep in mind that inferences come with a level of uncertainty and it’s important to consider factors such as sample size and diversity when making generalizations.