2. Lactation promotes a temporary loss of bone mass to provideadequate

amounts of calcium for milk production. Consider the data ontotal

body bone mineral content for a sample both during lactation (L)and

in the post weaning period (P).

1 . 2    3 4 5   6    7 8    9   10

L 1928 2549 2825 1924 1628 2175 2114 2621 1843 2541

P 2126 2885 2895 1942 1750 2184 2164 2626 2006 2627

Does the data suggest that true average total body bone mineralcon-

tent during post weaning exceeds that during lactation by morethan

25g? Use results from an output you obtained from the R softwareto

state and test the appropriate hypotheses with 95% confidencelevel(show

all details of R, either print our the R code and result orhand-write

R code and result ). State any assumptions required for the testto be

valid.

5. The following table summarizes the skin colours and positionof 368

NBA players in 2014. Suppose that an NBA player is randomlyselected

from that years player pool.

2

Guard positionForward Center Total

white 26 30    28 84

skin colour black 128 122    34   284

Total 154 152    62    368

(a) Find out where the variable \"skin colour\" is independentwith the

variable \"position\" with

alpha = 0.05

(b) We only concern about the variable \"position\". The mediaclaims

that the proportion of \"Guard\" is the same as the proportion of\"For-

ward\", which is twice as the proportion of \"Center\". Conduct atest to

find out whether the statement is valid with 90% confidenceinterval.

(hint: to test H0: P1= 0.4, P2 = 0.4, P3= 0.2)

6. Complete the following ANOVA table ( find the value of ?1,?2, ?3, ?4,

?5) [5] and give the null hypothesis and the alternativehypothesis, [2]

give your conclusion based on the ANOVA table [2].

ANOVA table

Df SumSq Mean Sq F value P value

brands 3 39.757 ?1 ?5 5.399e-07

Error    36 ?2 ?3

Total    ?4 . 68.128

7. Refer to the

Bulletin of Marine Science (April 2010)

study of teams

of shermen shing for the red apiny lobster in Baja ValiforniaSur,

Mexico. Two variables measured for each of 8 teams from thePunta

Abreojos shing cooperative were y=total catch of lobsters (inkilo-

grams) during the season and x=average percentage of trapsallocated

per day to exploring areas of unknown catch (called searchfrequency)

total catch search frequency

2785 35

6535 21

6695    26

4891    29

4937    23

5727    17

7019 21

5735 20

(a) Graph the data in a scatterplot (using R). What type oftrend, if any,

could be observed?

(b) Add the regression line to the plot (using R, eitherhand-write the R

code and plot the graph or print your R code and graph).

(c)Give the null and alternative hypothesis for testing whethertotal catch

is negatively linearly related to search frequency. Find thep-vale of the test

and give the appropriate conclusion of the test using alpha =0.05

(d) what's the coefficient of correlation between total catchand search

frequency?