Question

1. A researcher is interested in determining whether typists are most productive in the morning, at midday, in the evening, or late at night. To answer this question, the researcher recruits 20 participants and assigns 5 participants to be measured at each time of day. To evaluate productivity, the researcher measures words typed per minute at each time of day. Answer the following questions considering the data below (alpha = .05)

   	Morning	Midday	Evening	Night
   	99	42	80	82
   	80	32	83	78
   	99	45	94	79
   	98	49	70	97
   	79	38	79	96
   Mean	91	41.2	81.2	86.4
   SStotal =	9094.95

   What are the degrees of freedom for the numerator of the F-ratio?

   		2
   		3
   		16
   		19

2. A researcher is interested in determining whether typists are most productive in the morning, at midday, in the evening, or late at night. To answer this question, the researcher recruits 20 participants and assigns 5 participants to be measured at each time of day. To evaluate productivity, the researcher measures words typed per minute at each time of day. Answer the following questions considering the data below (alpha = .05)

   	Morning	Midday	Evening	Night
   	99	42	80	82
   	80	32	83	78
   	99	45	94	79
   	98	49	70	97
   	79	38	79	96
   Mean	91	41.2	81.2	86.4
   SStotal =	9094.95

   What are the degrees of freedom for the denominator of the F-ratio?

   		2
   		3
   		16
   		19

3. A researcher is interested in determining whether typists are most productive in the morning, at midday, in the evening, or late at night. To answer this question, the researcher recruits 20 participants and assigns 5 participants to be measured at each time of day. To evaluate productivity, the researcher measures words typed per minute at each time of day. Answer the following questions considering the data below (alpha = .05)

   	Morning	Midday	Evening	Night
   	99	42	80	82
   	80	32	83	78
   	99	45	94	79
   	98	49	70	97
   	79	38	79	96
   Mean	91	41.2	81.2	86.4
   SStotal =	9094.95

   What is the critical F value for this analysis?

   		3.24
   		4.46
   		6.04
   		19.00

4. A researcher is interested in determining whether typists are most productive in the morning, at midday, in the evening, or late at night. To answer this question, the researcher recruits 20 participants and assigns 5 participants to be measured at each time of day. To evaluate productivity, the researcher measures words typed per minute at each time of day. Answer the following questions considering the data below (alpha = .05)

   Morning	Midday	Evening	Night
   99	42	80	82
   80	32	83	78
   99	45	94	79
   98	49	70	97
   79	38	79	96
   Mean	91	41.2	81.2	86.4
   SStotal =	9094.95

   What is the SSwithin value?

   		360.58
   		1260.80
   		7834.15
   		9094.95

5. A researcher is interested in determining whether typists are most productive in the morning, at midday, in the evening, or late at night. To answer this question, the researcher recruits 20 participants and assigns 5 participants to be measured at each time of day. To evaluate productivity, the researcher measures words typed per minute at each time of day. Answer the following questions considering the data below (alpha = .05)

   Morning	Midday	Evening	Night
   99	42	80	82
   80	32	83	78
   99	45	94	79
   98	49	70	97
   79	38	79	96
   Mean	91	41.2	81.2	86.4
   SStotal =	9094.95

   What is the observed test statistic; in other words, what is the value of the F-ratio?

   		4.56
   		10.33
   		26.75
   		33.14

6. A researcher is interested in determining whether typists are most productive in the morning, at midday, in the evening, or late at night. To answer this question, the researcher recruits 20 participants and assigns 5 participants to be measured at each time of day. To evaluate productivity, the researcher measures words typed per minute at each time of day. Answer the following questions considering the data below (alpha = .05)

   Morning	Midday	Evening	Night
   99	42	80	82
   80	32	83	78
   99	45	94	79
   98	49	70	97
   79	38	79	96
   Mean	91	41.2	81.2	86.4
   SStotal =	9094.95

   What decision should be made regarding the null hypothesis?

   		Reject the null hypothesis
   		Retain the null hypothesis
   		Prove the null hypothesis

Answer 1

Number of Columns = k = 4

Total Number Of Observations = N = 20

(1) Df Numerator = k - 1 = 4 - 1 = 3 (Option 3)

(2) Df Denominator = N - k = 20 - 4 = 16 (Option 3)

(3) The F critical Value for df N = 3 and df D = 16 is Option 1: 3.24

(4) SS Within = SUM [ n * (Mean - GM)²]

GM = (91 + 41.2 + 81.2 + 86.4) / 4 = 299.8 = 79.95

Therefore SS within = 5 * (91 - 79.5)² + 5 * (41.2 - 79.5)² + 5 * (81.2 - 79.5)² + 5 * (86.4 - 79.5)² = 7834.15 (Option 3)

________________________

(5) To Calculate the test statistic, we need MS Within / MS Error

MS within = SS within / df Numerator = 7834.15 / 3 = 2611.38

SSerror = SS Total - SS within = 9094.95 - 2611.38 = 1260.88

MS Error = SS error / df Denominator = 1260.88 / 16 = 78.8

Therefore F = 2611.38 / 78.8 = 33.14 (Option 4)

_________________________

(6) Since F stat is > Fcritical, Option 1: reject The Null Hypothesis.

______________________________

The ANOVA Table is below for your reference

Source	SS	DF	Mean Square	F	Fcv	p
Between	7834.15	3	2611.38	33.14	3.24	0.0000
Within/Error	1260.80	16	78.80
Total	9094.95	19