The fat content of 7 randomly selected hot dogs was measured as follows: 16.3, 1

Question

The fat content of 7 randomly selected hot dogs was measured as follows:

16.3, 17.1, 13.3, 12.0, 8.5, 17.9, 17.1

It is reasonable to treat these measurements as coming from a normal distribution with unknown mean and unknown variance

2

a)Use the data to calculate an unbiased point estimate of the true mean, , of hot dog fat content.  

b)Use the data to find an unbiased point estimate of the population variance,

2

of hot dog fat content  

c) Find the sample standard deviation of the above data  

d)Create a 98% confidence interval for . (

,

)

e) What critical value did you use to calculate the 98% confidence interval in d?  

f)Create a 98% prediction interval for . (

,

)

Explanation / Answer

Solutiona:

point estimate of the true mean, is sample mean

sample mean= 14.6

Solutionb:

unbiased point estimate of the population variance=sample variance

= 11.99

Solutionc:

the sample standard deviation of the above data  

=3.462658

SOlutond:

98% confidence interval for

10.487 and 18.713

( 10.487 ,18.713)

USed R code:

fatcontent <- c(16.3, 17.1, 13.3, 12.0, 8.5, 17.9, 17.1)
mean(fatcontent)
var(fatcontent)
sd(fatcontent)
t.test(fatcontent,conf.level=0.98)

Output:

One Sample t-test

data: fatcontent

t = 11.156, df = 6, p-value = 3.095e-05

alternative hypothesis: true mean is not equal to 0

98 percent confidence interval:

10.487 18.713

sample estimates:

mean of x

14.6

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