Question

A tea drinker’s society estimates that the mean consumption of tea by a person in the United States is more than 8 gallons per year. In a random sample of 100 people, you find that the mean consumption of tea is 7.9 gallons per year with a standard deviation of 2.67 gallons. At the 7% level significance, can you support the society’s claim?

Answer 1

Since the sample size is 100 hence we use Z statistic here,

Ho : u=8

Ha: u>8

Rejection region:

Reject Ho if p value calculated is less than 0.07 or the -Z calculated is greater than Z at 93% confidence level.

Test statistics:

$Z=\frac{M-u}{\frac{s}{\sqrt{n}}}$

Here M=sample mean=7.9

S =Standard deviation= 2.67

n=100

Z = -0.3745

P value :

P value associated with Z statistic is calculated using Z statistic table or calculator as 0.354.

Conclusion: with p value approach

Since the p value is greater than the level of significance that is 0.07 hence we fail to reject the null hypothesis , so we conclude that at 7 % level of significance we do not have enough evidence to support the claim of consumption of tea is more than 8 gallon per year.