Time of Day Time (sec) Time of Day Time (sec) Time of Day Time (sec) Early (7 a.m.) 68 Evening (5 p.m.) 299 Late Night (12 a.m.) 216 Early (7 a.m.) 138 Evening (5 p.m.) 367 Late Night (12 a.m.) 175 331 Late Night (12 a.m.) 274 Early (7 a.m.) Early (7 a.m.) 75 Evening (5 p.m.) Evening (5 p.m.) 186 257 Late Night (12 a.m.) Late Night (12 a.m.) Late Night (12 a.m.) Late Night (12 a.m.) 171 Early (7 a.m.) 68 Evening (5 p.m.) 260 187 Early (7 a.m.) 217 Evening (5 p.m.) 269 213 Early (7 a.m.) Early (7 a.m.) 93 Evening (5 p.m.) Evening (5 p.m.) Evening (5 p.m.) 252 221 90 200 Late Night (12 a.m.) Late Night (12 a.m.) 139 Early (7 a.m.) 71 296 226 Early (7 a.m.) 154 Evening (5 p.m.) 204 Late Night (12 a.m.) 128 166 190 Early (7 a.m.) Early (7 a.m.) Early (7 a.m.) Early (7 a.m.) Early (7 a.m.) Evening (5 p.m.) Evening (5 p.m.) Evening (5 p.m.) Evening (5 p.m.) Late Night (12 a.m.) Late Night (12 a.m.) Late Night (12 a.m.) Late Night (12 a.m.) Late Night (12 a.m.) 236 130 240 128 72 350 217 81 256 196 76 Evening (5 p.m.) 282 201 Early (7 a.m.) 129 Evening (5 p.m.) 320 Late Night (12 a.m.) 161
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Cereals, redux We also have data on the protein content
of the cereals in Exercise 19 by their shelf number. Here
are the boxplot and ANOVA table:a) What are the null and alternative hypotheses?
b) What does the ANOVA table say about the null
hypothesis? (Be sure to report this in terms of
protein content and shelves.)
c) Can we conclude that cereals on shelf 2 have a lower
mean protein content than cereals on shelf 3? Can we
conclude that cereals on shelf 2 have a lower meanprotein content than cereals on shelf 1? What can we
conclude?
d) To check for significant differences between the shelf
means we can use a Bonferroni test, whose results are
shown below. For each pair of shelves, the difference
is shown along with its standard error and significance
level. What does it say about the questions in part c?
Dependent Variable: PROTEIN
(I)
Shelf
(J)
Shelf
Mean
Difference
(I-J)
Std.
Error P-Value
95%
Confidence
Interval
Bonferroni Lower
Bound
Upper
Bound
1 2 0.75 0.322 0.070 -0.04 1.53
3 -0.21 0.288 1.000 -0.92 0.49
2 1 -0.75 0.322 0.070 -1.53 0.04
3 -0.96(*) 0.283 0.004 1.65 0.26
3 1 0.21 0.288 1.000 -0.49 0.92
2 0.96(*) 0.283 0.004 0.26 1.65
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