The accompanying data are the weights (kg) of poplar trees that were obtained from trees planted in a rich and moist region. The trees were given different treatments identified in the accompanying table. Also shown are partial results from using the Bonferroni test with the sample data. Complete parts (a) through (c).

Question content area bottom

Part 1

a. Use a

0.100.10

significance level to test the claim that the different treatments result in the same mean weight.

Determine the null and alternative hypotheses.

Upper H 0H0:

mu 1 greater than mu 2 greater than mu 3 greater than mu 41>2>3>4

mu 1 equals mu 2 equals mu 3 equals mu 41=2=3=4

Not all of the population means are equalNotallofthepopulationmeansareequal

At least two of the population means are equalAtleasttwoofthepopulationmeansareequal

mu 1 not equals mu 2 not equals mu 3 not equals mu 41234

Exactly two of the population means are equalExactlytwoofthepopulationmeansareequal

Upper H 1H1:

mu 1 not equals mu 2 not equals mu 3 not equals mu 41234

mu 1 greater than mu 2 greater than mu 3 greater than mu 41>2>3>4

mu 1 equals mu 2 equals mu 3 equals mu 41=2=3=4

At least two of the population means are equalAtleasttwoofthepopulationmeansareequal

At least one of the four population means is different from the othersAtleastoneofthefourpopulationmeansisdifferentfromtheothers

Exactly two of the population means are different from the othersExactlytwoofthepopulationmeansaredifferentfromtheothers

Part 2

Determine the test statistic.

The test statistic is

enter your response here.

(Round to two decimal places as needed.)

Part 3

Determine the P-value.

The P-value is

enter your response here.

(Round to three decimal places as needed.)

Part 4

What is the conclusion for this hypothesis test at a

0.100.10

significance level?

A.

RejectReject

Upper H 0H0.

There is

sufficientsufficient

evidence to warrant rejection of the claim that the four different treatments yield the same mean poplar weight.

B.

RejectReject

Upper H 0H0.

There is

insufficientinsufficient

evidence to warrant rejection of the claim that the four different treatments yield the same mean poplar weight.

C.

Fail to rejectFailtoreject

Upper H 0H0.

There is

insufficientinsufficient

evidence to warrant rejection of the claim that the four different treatments yield the same mean poplar weight.

D.

Fail to rejectFailtoreject

Upper H 0H0.

There is

sufficientsufficient

evidence to warrant rejection of the claim that the four different treatments yield the same mean poplar weight.

Part 5

b. What do the displayed Bonferroni results tell us?

With a P-value of

enter your response here,

there

is not

is

a significant difference between the No Treatment and Fertilizer groups.

With a P-value of

enter your response here,

there

is

is not

a significant difference between the No Treatment and Irrigation groups.

With a P-value of

enter your response here,

there

is

is not

a significant difference between the No Treatment and Fertilizer and Irrigation groups.

(Round to three decimal places as needed.)

Part 6

c. Let

mu 11,

mu 22,

mu 33,

and

mu 44

represent the mean amount of the no treatment, fertilizer, irrigation, and fertilizer and irrigation groups, respectively. Use the Bonferroni test procedure with a

0.100.10

significance level to test for a significant difference between the mean amount of the irrigation treatment group and the group treated with both fertilizer and irrigation. Identify the test statistic and the P-value. What do the results indicate?

Determine the null and alternative hypotheses.

Upper H 0H0:

mu 3 not equals mu 434

mu 2 not equals mu 323

mu 1 not equals mu 212

mu 3 equals mu 43=4

mu 2 equals mu 32=3

mu 1 equals mu 21=2

Upper H 1H1:

mu 2 not equals mu 323

mu 3 equals mu 43=4

mu 1 not equals mu 212

mu 3 not equals mu 434

mu 1 equals mu 21=2

mu 2 equals mu 32=3

Part 7

The test statistic is

enter your response here.

(Round to two decimal places as needed.)

Part 8

Find the P-value.

The P-value is

enter your response here.

(Round to three decimal places as needed.)

Part 9

What do the results indicate at a

0.100.10

significance level?

A.

RejectReject

Upper H 0H0.

There is

insufficientinsufficient

evidence to warrant rejection of the claim that the irrigation treatment group and the group treated with both fertilizer and irrigation yield the same mean poplar weight.

B.

Fail to rejectFailtoreject

Upper H 0H0.

There is

sufficientsufficient

evidence to warrant rejection of the claim that the irrigation treatment group and the group treated with both fertilizer and irrigation yield the same mean poplar weight.

C.

RejectReject

Upper H 0H0.

There is

sufficientsufficient

evidence to warrant rejection of the claim that the irrigation treatment group and the group treated with both fertilizer and irrigation yield the same mean poplar weight.

D.

Fail to rejectFailtoreject

Upper H 0H0.

There is

insufficientinsufficient

evidence to warrant rejection of the claim that the irrigation treatment group and the group treated with both fertilizer and irrigation yield the same mean poplar weight.

Upper H 0:Upper H 1Upper H 1:The test statistic is(Round to two decimal places as needed.)The P-value is(Round to three decimal places as needed.)What is the conclusion for this hypothesis test at a 0.10 significance level?With a P-value of, there, therea significant difference between the No Treatment and Fertilizer groups.With a P-value of, there, therea significant difference between the No Treatment and Irrigation groups.With a P-value of, there, there(Round to three decimal places as needed.)Upper H 0:Upper H 1Upper H 1:The test statistic is(Round to two decimal places as needed.)The P-value is(Round to three decimal places as needed.)What do the results indicate at a 0.10 significance level?