Question

Harbucks coffee claims that the average amount of caffeine in cups of their coffee is 180 mg. Randy wishes to check the validity of this claim, and so he obtains a random sample of 49 cups of Harbucks coffee, from which he obtains a sample mean and standard deviation of 181 mL and 1.2 mL. Randy also notes that the sample data exhibit strong right skewness, so he suspects the population is also right skewed

1. Does Randy have evidence to suggest the mean amount of caffeine in cups of Harbucks coffee is more than 180mL? Test at a 1% significance level

2. Are there any obvious threats to the assumptions needed for this test to be valid?

Answer 1

Sol:

Ho:mu=180

Ha:mu>180

alpha=0.01

test sattistic:

t=xbar-mu/s/sqrt(n)

t=(181-180)/(1.2/sqrt(49)

t=5.833333

df=n-1=49-1=48

p value ine xcel

=T.DIST.RT(5.833333,48)

=2.25061E-07

p value=0.0000

p<alpha

Reject Ho
Accept Ha

Randy have sufficient statistical evidence at 1% level of significance  to suggest the mean amount of caffeine in cups of Harbucks coffee is more than 180mL

Assumotions fot test:

simple independent random sample

sample follows normal distribution

Here n=49,n>30 large sample

sample follows normal distribution

sample is simple random sample

assumptions are satisfied