Part 3 Nutritional researchers are comparing the sodium levels of two different

Question

Part 3 Nutritional researchers are comparing the sodium levels of two different brands of canned black beans. They randomly select 5 cans from each of the two brands. The following are the observed sodium levels (in mg) Brand 1: 580, 592, 588, 589. 583 Brand 2: 579, 582, 577, 591. 581 Let 1,2 be the true mean sodium level for cans of black beans made by Brand 1, Brand 2 (respectively). (a) (1 mark) Using R, calculate and compare the standard deviations of the two samples Indicate whether you should use pooled procedures or unpooled procedures for these data (b) (1 mark) Give the command and output to test the hypotheses Ho : ?1-142-0, ??-112 0. (c) (1 mark) What is the p-value for our test? (d) (1 mark) What is the strength of evidence we have found against Ho?

Explanation / Answer

Solution1:

rocde :

Brand1 <- c(580,592,588,589,583)
Brand2 <- c(579,582,577,591,581)

sd(Brand1)
sd(Brand2)

output:

> sd(Brand1)
4.827007
> sd(Brand2)
5.385165

standard deviation of brand1=4.827007

standard deviation of brand2=5.385165

that is Brand1,Brand2 standard deviations are different.

Do not use pooled variance

Solutionb:

t test assuming unequal variances

rcode:

t.test(Brand1,Brand2)

output:

Welch Two Sample t-test

data: Brand1 and Brand2
t = 1.3605, df = 7.9061, p-value = 0.2112
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-3.073509 11.873509
sample estimates:
mean of x mean of y
586.4 582.0

solutionc:

t=1.3605

p=0.2112

solutiond:

p=0.2112

p>0.05

do not reject H0

Accept H0

no suffucient evidence to reject H0

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