Question

A researcher claims that the yearly consumption of soft drinks per person is 52 gallons. In a sample of 50 randomly selected people, the mean of the yearly consumption was 56.3. The standard deviation of the population is 3.5 gallons. Is the researchers claim valid when alpha is .01

Answer 1

Solution:

Hypothesis are

H0 : = 52

Ha : 52

Test statistic z = = [56.3 - 52]/[3.5/50] = 8.69

Test statistic = 8.69

Now ,

Here , TWO  tailed test

p value = P(Z < -z) + P(Z > +z) =  P(Z < -8.69) + P(Z > +8.69) = 0.0000+ 0.0000 = 0.0000

p value = 0.0000

P value is Less than = 0.01

We reject the null hypothesis

Conclusion:

There is sufficient evidence to reject the claim that the yearly consumption of soft drinks per person is 52 gallons.

i.e.  The researchers claim is not valid .