Question

Calculating the standard deviation and the estimated standard error for the sample mean difference A researcher is interested in hamster wheel-running activity during the summer versus the winter. She suspects that either the hamsters will run less during the winter to conserve energy or they will run more to keep warm. She records the activity of n = 16 hamsters during June, July, and August and compares their running-wheel revolutions per hour to the activity of the same hamsters during December, January, and February. The data are collected, and the results show an average difference score of M_D = 3.1 and a sum of squares of SS = 331.35. What is the value for degrees of freedom for this repeated-measures t test? a. 16 b. 37 c. 34 d. 15 What is the sample standard deviation (s) for the D scores? a. 4.7 b. 1.18 c. 331.35 d. 22.09 What is the estimated standard error of the mean difference (S_MD) for this study? a. 1.38 b. 0.26 c. 1.09 d. 1.18

Answer 1

Answer and Step-by-step explanation:

The answer is attached below

Answer 2

(a) Degree of freedom is "15".

(b) Standard deviation is "4.7".

(c) Standard error is "1.18".

Given:

• $n = 16$
• $M_D = 3.1$
• Sum of squares, $SS = 331.55$

(a)

The degree of freedom will be:

= $n-1$

= $16-1$

= $15$

(b)

The sample standard deviation,

= $\sqrt{\frac{SS}{n-1} }$

= $\sqrt{\frac{331.55}{15} }$

= $\sqrt{22.1033}$

= $4.7$

(c)

The standard error will be:

= $\frac{\sigma}{\sqrt{n} }$

= $\frac{4.7014}{\sqrt{16} }$

= $\frac{4.7014}{4}$

= $1.18$

Thus the above answers are right.

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