Question

For this assignment, please submit the answers to the following questions, as well as an Excel spreadsheet which documents the work you did.

Do poets die young? According to William Butler Yeats, “She is the Gaelic muse, for she gives inspiration to those she persecutes. The Gaelic poets die young, for she is restless, and will not let them remain long on earth.” One study designed to investigate this issue examined the age at death for writers from different cultures and genders. Three categories of writers examined were novelists, poets, and nonfiction writers. The ages at death for female writers in these categories from North America are given in the dataset on blackboard (data file : Female Writers.xls). Most of the writers are from the United States, but Canadian and Mexican writers are also included.

a)   Use Excel to build a boxplot of the three associated data sets. If the population mean death ages were the same for the three populations, would you expect to see a boxplot like this? Please elaborate.
b)   Write down both the null and alternative hypothesis for the one-way ANOVA.

c)   Run the one-way ANOVA test in Excel; make sure you save this in your spreadsheet somewhere where it can be found.

d)   You will see a value for F-stat. Report this value, and explain how it is related to MSA and MSW.

e)   In general, what is a p-value? In your table, what p-value is reported, and what exactly does it mean?

f)   At the .05 level of significance, is there evidence of a difference in mean age of death among the various types of female writers? Explain your decision.

Novels	Poems	Nonfiction
57	88	74
90	69	86
67	78	87
56	68	68
90	72	76
72	60	73
56	50	63
90	47	78
80	74	83
74	36	86
73	87	40
86	55	75
53	68	90
72	75	47
86	78	91
82	85	94
74	69	61
60	38	83
79	58	75
80	51	89
79	72	77
77	58	86
64	84	66
72	30	97
88	79
75	90
79	66
74	45
85	70
71	48
78	31
57	43
54
50
59
72
60
77
50
49
73
39
73
61
90
77
57
72
82
54
62
74
65
83
86
73
79
63
72
85
91
77
66
75
90
35
86

Answer 1

a) Boxplot:

1) Boxplot for novels:

here Q1=61 ;Median=73; Q3=80; IQ range=19; N=67 No outlier in this data

2) Boxplot for poems:

here Q1=48.5 ; Median=68: Q3=77.25; IQ range=28.75,N=32 No outlier

3) Boxplot for Nonfiction

here Q1= 69.25; Median=77.5 ; Q3=86.75 ; IQ range= 17.5; N=24 there is one outlier=40
A) Hypothesis:

Null hypothesis: H0:

Alternative hypothesis:H1: Not H0

Test statistics:

F=MSG/MSE

Decision rule:

Reject H0 if F> F(n-1)(n-k)0.05

Hypothesis testing using MS-excel:

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Novels	67	4787	71.44776	170.3419
Poems	32	2022	63.1875	299.1895
Nonfiction	24	1845	76.875	198.7228
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	2744.193	2	1372.096	6.562944	0.001973	3.071779
Within Groups	25088.07	120	209.0672
Total	27832.26	122

Conclusion:

here F value 6.5629>3.0717 also here p-value 0.0019<0.05 so we reject H0 and conclude that there is a statistically significant difference between these three groups( Novel, poems, and nonfiction)