Question

2. Lactation promotes a temporary loss of bone mass to provide adequate

amounts of calcium for milk production. Consider the data on total

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 mineral con-

tent during post weaning exceeds that during lactation by more than

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

state and test the appropriate hypotheses with 95% confidence level(show

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

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

valid.

5. The following table summarizes the skin colours and position of 368

NBA players in 2014. Suppose that an NBA player is randomly selected

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 independent with the

variable "position" with

alpha = 0.05

(b) We only concern about the variable "position". The media claims

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

ward", which is twice as the proportion of "Center". Conduct a test to

find out whether the statement is valid with 90% confidence interval.

(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 alternative hypothesis, [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 Valifornia Sur,

Mexico. Two variables measured for each of 8 teams from the Punta

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

grams) during the season and x=average percentage of traps allocated

per day to exploring areas of unknown catch (called search frequency)

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 of trend, if any,

could be observed?

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

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

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

is negatively linearly related to search frequency. Find the p-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 catch and search

frequency?

Answer 1

## Question 2

# It is a paired t-test, the corresponding R command is given below.

L=c(1928, 2549, 2825, 1924, 1628, 2175, 2114, 2621, 1843, 2541)

P=c(2126, 2885, 2895, 1942, 1750, 2184, 2164, 2626, 2006, 2627)

t.test(x=L, y = P,
alternative = "less",
mu = 25, paired = TRUE, conf.level = 0.95)

## End Command

## Run output

> L=c(1928, 2549, 2825, 1924, 1628, 2175, 2114, 2621, 1843, 2541)
>
> P=c(2126, 2885, 2895, 1942, 1750, 2184, 2164, 2626, 2006, 2627)
>
> t.test(x=L, y = P,
+ alternative = "less",
+ mu = 25, paired = TRUE, conf.level = 0.95)

Paired t-test

data: L and P
t = -3.9801, df = 9, p-value = 0.001603
alternative hypothesis: true difference in means is less than 25
95 percent confidence interval:
-Inf -45.50299
sample estimates:
mean of the differences
-105.7

## End output.

State any assumptions required for the test to be valid.

Ans: The assumption required for the test to be valid is that the difference of the L-P should follow a normal distribution.