Using the Following Data, Conduct a Two-Tailed T-Test

question 21

Short Answer

Using the following data, conduct a two-tailed t-test.Use a known population mean of 49 and α = .05.
55 48 59 50 48 52 50 48 57 54
50 52 54 43 44 53 40 46 50 51 $\begin{array}{l}\bar{X}=\frac{1004}{20}=50.2 \\\\s_{X}^{2}=\frac{50818-\frac{(1004)^{2}}{20}}{20-1}=\frac{417.2}{19}=21.958 \\\\s_{X}=\sqrt{21.958}=4.69 \\\\s_{\bar{X}}=\frac{4.69}{\sqrt{20}}=1.05 \\\\t_{\text {obt }}=\frac{50.2-49}{1.05}=+1.14 \\\\t_{\text {crit }}=\pm 2.093\end{array}$

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Definitions:

Old Age

Old age is the latter part of life, typically defined as the period after retirement, or around the age of 65, characterized by both physical and cognitive changes.

Middle Adulthood

A stage of life typically ranging from about 40 to 65 years old, marked by increased personal and professional achievements, awareness of mortality, and often a focus on legacy.

Young Adulthood

A developmental stage typically referring to individuals aged between 18 to 40 years, characterized by exploration of personal and professional identities.

Cognitive Development

The growth and change in intellectual capacities, such as thinking, reasoning, and understanding, throughout the lifespan.