Question

ot camp. Summary statistics on BMI maasuraments are shown in thetabla to tha right Camplato partsathrough h Mesn Deviation Starting BMI 34.4 7.1 Ending EMI 307 64 Differences 3.71.5 a. Ghe tha nul and altemative hypothesas for datarmining whether the mean BMI at the and of camp i less than tha mean DMI at the start of camp Le ul be th population mean BMI at the start oic mp μ2 be the population mean BMl at the end of c pand μο-μι-u2 Choosc the carrect answer below. O A. Usa an indapandant-samplas t-test bacausa the sampla ot dittarances was chasan randomy o c use an independent sa ies t test because the sample sze i greater dMm30. By the Cental Limit Theorem O D. Usa a pairad-diteranca t-tast because the assumption at indpandant samplas is invald c. Celcuate the teat statistic using the formula for an independent-samplea tHeet this con tion guarantees the test statist will be appro mate y normal. Round to two decimal places as needed.] d. Calculate the test stadcic using the formula for paired-dtficranco 1 toct t(Round ta twvo dacimal placs as nad e. Compare the lest 밝비 1K8. parts C 비nd d which test st stK provides more ewdenue m support of the sitermative hypothesis? O A. he tast statistic using the tommula tor an independent-samples t-t st O B. The test stelislic using the omule for peie-siTerence tes f. The p-value of the test, part d, was reported as p<0.0001. Interpret this result assuming -0.01 H because the p-ve is the sign ficance level. There i evidence that the mean B at the end oi camp is the mean E at the start of camp

Answer 1

Here, we have given that

n= number of campers =74

$\bar x1$= mean starting BMI = 34.4

$\bar x2$=mean ending BMI= 30.7

S1= starting BMI standard deviation = 7.1

S2= ending BMI standard deviation = 6.4

$\bar d$= Mean difference= 3.7

S.D(diff) =standard deviation of difference = 1.5

Claim: To check whether the mean BMI at the end of camp is less than the mean BMI at the end of camp.

The Hypothesis is

Ho: \mu d= 0

v/s

H1: \mu d < 0

Here, we use paired difference t test because the assumptions of independent sample is invalid

and data is in pre and post format.

Now,

Now, we can find the test statistic

, stat = sd

2 7 , stat = V(74)

=21.22

we get test statistic is 21.22

the test statistics using the formula for paired difference t-test

Degrees of freedom = n-1= 74-1=73

$\alpha$= level of significance=0.01

Now, we can find the P-value

P-value = 0.0000 ( using EXCEL =TDIST(x,D.F,tail=1))

Decision:

P-value < 0.01 ($\alpha$)

Conclusion:

That is we fail to reject Ho (Null Hypothesis) because P-value < 0.01 ($\alpha$)

There is not sufficient evidence that the mean BMI at the end of camp is less than the mean BMI at the end of camp.

9. option A is correct that Yes , in order to make the valid small sample inferences about $\mu_d$ the differences need to be normally distributed.

(B)

Now,

Formula for CI is as follows

In)

First we find the critical value

Degrees of freedom = n-1 = 74-1 = 73

$\alpha$= level of significance=0.01

We get

Tc= 2.645 ( using t table)

Now,

In)

-2.645 * _15 (74) 1.5 ud 3.7+2615 V(74)

2.24く,ld < 5.16

Interpretation:

This confidence interval shows that we are 99% confident that the difference in the population mean will falls under this interval.