Question

The file FastFood contains the amount that a sample of fif- teen customers spent for lunch ($) at a fast-food restaurant:

7.42 6.29 5.83 6.50 8.34 9.51 7.10 6.80 5.90 4.89 6.50 5.52 7.90 8.30 9.60

1. At the 0.05 level of significance, is there evidence that the mean amount spent for lunch is different from $6.50?

2. Determine the p-value in (a) and interpret its meaning.

3. What assumption must you make about the population distribu-

   tion in order to conduct the t test in (a) and (b)?

4. Because the sample size is 15, do you need to be concerned about the shape of the population distribution when conducting

   the t test in (a)? Explain.

Answer 1

Sol:

Ho:

Ha:

alpha=0.05

For the given sample

sample mean=xbar= 7.093333

sample standard deviation=s= 1.406031

sample size=n-15

t=xbar-mu/s/sqrt9n)

=(7.093333-6.50)/(1.406031/sqrt(15)

t=1.634366

df=n-1=5-1=14

Determine the p-value in (a) and interpret its meaning.

p value in excel is

=T.DIST.2T(1.634366,14)

p=0.124459709

p>0.05

Fail to reject Ho

Accept Ho

There is insufficient evidence at 5% level of significance to support the claim that the mean amount spent for lunch is different from $6.50

What assumption must you make about the population distribu-

tion in order to conduct the t test in (a) and (b)?

sample is simple random sample

sample should follow normal distribution

Because the sample size is 15, do you need to be concerned about the shape of the population distribution when conducting

the t test in (a)

As sample size ,n=15,n<30

Accprding to central limit theorem,large sample (n>30),sample follows normal distribution,

but here n<30,n-15

sample do not follow normal distribution